optical thickness retrievals of subtropical cirrus and ... · optical thickness retrievals of...

Optical Thickness Retrievals of

Subtropical Cirrus and Arctic

Stratus from Ground-Based and

Airborne Radiance Observations

Using Imaging Spectrometers

Der Fakultat fur Physik und Geowissenschaften

der Universitat Leipzig

eingereichte

DISSERTATION

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

(Dr. rer. nat.)

vorgelegt

von Dipl.-Met. Michael Schafer

geboren am 27.02.1985 in Schonebeck/ Elbe, Sachsen-Anhalt

Leipzig, den 22.02.2016

Bibliographische Beschreibung:

Schafer, Michael

Optical Thickness Retrievals of Subtropical Cirrus and Arctic Stratus from Ground-

Based and Airborne Radiance Observations Using Imaging Spectrometers

Universitat Leipzig, Dissertation

121 S., 128 Lit., 49 Abb., 16 Tab.

Referat:

Im folgenden wird die Entwicklung und Anwendung neuer Ableitungsverfahren von

Wolkenparametern, basierend auf bodengebundenen und flugzeuggetragenen spektralen

Strahldichtemessungen uber heterogenen Oberflachen, vorgestellt und das Fernerkundungs-

potential abbildender Spektrometer evaluiert. Die spektralen Strahldichtefelder wur-

den wahrend zweier internationaler Feldkampagnen im sichtbaren Wellenlangenbereich

(400–970 nm) mit hoher raumlich Auflosung (< 10m) gemessen. Bodengebundene Messun-

gen wurden verwendet, um hohe Eiswolken zu beobachten, flugzeuggetragene, um arktischen

Stratus zu beobachten. Aus den Messungen werden raumlich hochaufgeloste wolkenoptische

Dicken abgeleitet und anschließend horizontale Wolkeninhomogenitaten untersucht. Die

Ableitung der wolkenoptischen Dicke birgt je nach Messkonfiguration verschiedene Unsicher-

heiten. Eine Reduzierung der Unsicherheiten wird durch die Vorgabe einer Eiskristallform

zur Verbesserung der Ableitung der optischen Dicke hoher Eiswolken erreicht. Diese wer-

den unabhangig aus den winkelabhangigen, in das gemessene Strahldichtefeld eingepragten

Eigenschaften der Streuphasenfunktion, abgeleitet. Bei Vernachlassigung dieser Information

und Wahl der falschen Eiskristallform, treten Fehler in der abgeleiteten optischen Dicke von

bis zu 90% auf. Bei der Fernerkundung von arktischem Stratus beeinflusst die sehr vari-

able Bodenalbedo die Genauigkeit der Ableitung der optischen Dicke. Beim Ubergang von

Meereis zu Wasser, findet die Abnahme der reflektierten Strahldichte im bewolktem Fall

nicht direkt uber der Eiskante, sondern horizontal geglattet statt. Allgemein reduzieren

Wolken die reflektierte Strahldichte uber Eisflachen nahe Wasser, wahrend sie uber dem

Wasser erhoht wird. Dies fuhrt zur Uberschatzung der wolkenoptischen Dicke uber Wasser-

flachen nahe Eiskanten von bis zu 90%. Dieser Effekt wird mit Hilfe von Beobachtungen

und dreidimensionalen Strahlungstransferrechnungen untersucht und es wird gezeigt, dass

sein Einfluss noch bis zu 2200m Entfernung zur Eiskante wirkt (fur Meeresalbedo 0.042 und

Meereisalbedo 0.91 bei 645 nm Wellenlange) und von den makrophysikalischen Wolken- und

Meereiseigenschaften abhangt.

Die abgeleiteten Felder der optischen Dicke werden statistisch ausgewertet, um die Inho-

mogeneitat der Wolken zu charakterisieren. Autokorrelationsfunktionen und Leistungs-

dichtespektren zeigen, dass Inhomogenitaten vonWolken mit vorranging richtungsabhangiger

Struktur nicht mit einem allgemeingultigen Parameter beschrieben werden konnen. Es sind

Inhomogenitatsmaße entlang und entgegen der jeweiligen Wolkenstrukturen notig, um Fehler

von bis zu 85% zu vermeiden.

ii

Bibliographic Description:

Schafer, Michael

Optical Thickness Retrievals of Subtropical Cirrus and Arctic Stratus from Ground-

Based and Airborne Radiance Observations Using Imaging Spectrometers

University of Leipzig, Dissertation

121 p., 128 ref., 49 fig., 16 tab.

Abstract:

The development and application of new cloud retrieval methods from ground–based and air-

borne measurements of spectral radiance fields above heteorogeneous surfaces is introduced.

The potential of imaging spectrometers in remote–sensing applications is evaluated. The

analyzed spectral radiance fields were measured during two international field campaigns

in the visible wavelength range (400–970 nm) with high spatial (< 10m) resolution. From

ground–based measurements, high ice clouds were observed and from airborne measurements

Arctic stratus. From the measurements, cloud optical thickness is retrieved with high spa-

tial resolution and the horizontal cloud inhomogeneities are investigated. Depending on the

measurement configuration, different uncertainties arise for the retrieval of the cloud optical

thickness. A reduction of those uncertainties is derived by a specification of the ice crystal

shape to improve the retrieval of the optical thickness of high ice clouds. The ice crystal shape

is obtained independently from the angular information of the scattering phase function fea-

tures, imprinted in the radiance fields. A performed sensitivity study reveals uncertainties

of up to 90%, when neglecting this information and applying a wrong crystal shape to the

retrieval. For remote-sensing of Arctic stratus, the highly variable surface albedo influences

the accuracy of the cloud optical thickness retrieval. In cloudy cases the transition of re-

flected radiance from open water to sea ice is not instantaneous but horizontally smoothed.

In general, clouds reduce the reflected radiance above bright surfaces in the vicinity of open

water, while it is enhanced above open sea. This results in an overestimation of to up to

90% in retrievals of the optical thickness. This effect is investigated. Using observations

and three-dimensional radiative transfer simulations, this effect is quantified to range to up

to 2200m distance to the sea-ice edge (for dark-ocean albedo of αwater = 0.042 and sea-ice

albedo of αice = 0.91 at 645 nm wavelength) and to depend on macrophysical cloud and

sea-ice properties.

The retrieved fields of cloud optical thickness are statistically investigated. Auto–correlation

functions and power spectral density analysis reveal that in case of clouds with prevailing

directional cloud structures, cloud inhomogeneities cannot be described by a universally valid

parameter. They have to be defined along and across the prevailing cloud structures to avoid

uncertainties up to 85%.

Contents iii

Contents

1 Motivation and Objectives 1

1.1 The Advantage of High Spatial Resolution . . . . . . . . . . . . . . . . . . . . 1

1.2 Observation of Cloud Inhomogenieties by Remote Sensing . . . . . . . . . . . 3

1.3 Complications of Retrievals of Cirrus Properties . . . . . . . . . . . . . . . . . 4

1.4 Current Limitations for Arctic Stratus Cloud Retrieval . . . . . . . . . . . . . 6

1.5 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Definitions 9

2.1 Radiative Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Cloud Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Extinction Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Single–Scattering Albedo . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.3 Scattering Phase Function . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.4 Cloud Optical Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Cloud Microphysical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Experimental 17

3.1 Imaging Spectrometer AisaEAGLE . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.2 Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Calibrations and Data Handling . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.1 Radiometric Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.2 Dark Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.3 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.4 Spectral Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.5 Measurement Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.6 Smear correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Observation Geometries and Scattering Angle Derivation . . . . . . . . . . . 28

4 Subtropical Cirrus - Ground-Based Observations 33

4.1 CARRIBA (Clouds, Aerosol, Radiation, and tuRbulence in the trade wInd

regime over BArbados) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Method to Retrieve Cirrus Optical Thickness . . . . . . . . . . . . . . . . . . 34

4.3 Measurement Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 Retrieval of Ice Crystal Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.5 Retrieval Results for Cirrus Optical Thickness . . . . . . . . . . . . . . . . . . 41

4.6 Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

iv Contents

5 Arctic Stratus - Airborne Observations 47

5.1 VERDI (VERtical Distribution of Ice in Arctic clouds) . . . . . . . . . . . . . 47

5.2 Identification of Ice and Open Water . . . . . . . . . . . . . . . . . . . . . . . 49

5.3 Quantification of 3D Radiative Effects from Measurements . . . . . . . . . . . 51

5.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.4.1 3D Radiative Transfer Model . . . . . . . . . . . . . . . . . . . . . . . 57

5.4.2 Case I: Infinitely Straight Ice Edge . . . . . . . . . . . . . . . . . . . . 58

5.4.3 Case II: Single Circular Ice Floes . . . . . . . . . . . . . . . . . . . . . 62

5.4.4 Case III: Groups of Ice Floes . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.5 Case IV: Realistic Sea-Ice Scenario . . . . . . . . . . . . . . . . . . . . 67

5.5 Sensitivity of τst and reff derived from Synthetic Cloud Retrieval . . . . . . . 69

5.6 Cloud Optical Thickness Retrieval . . . . . . . . . . . . . . . . . . . . . . . . 71

6 Directional Structure of Cloud Inhomogeneities 75

6.1 Analysis with 1D Inhomogeneity Parameters . . . . . . . . . . . . . . . . . . 75

6.2 Spatial 2D Auto-Correlation and De-Correlation Length . . . . . . . . . . . . 77

6.3 Power Spectral Density Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 80

7 Summary and Conclusions 85

7.1 Subtropical Cirrus Optical Thickness Retrieval from Ground–Based Observa-

tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.2 Arctic Stratus Cloud Retrieval from Airborne Observations . . . . . . . . . . 86

7.3 Cloud Inhomogeneity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7.4 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Bibliography 91

List of Greek Symbols 101

List of Latin Symbols 103

List of Abbreviations 107

List of Figures 109

List of Tables 111

Acknowledgements 112

Curriculum Vitae 114

1

1 Motivation and Objectives

The globally and annually averaged cloud cover is about 70% (Rossow and Schiffer, 1999).

Therefore, clouds need to be considered as an important regulator of the Earth’s radiation

budget (Loeb et al., 2009). Clouds scatter and absorb solar radiation in the wavelength range

from 0.2 to 5 µm; they emit and absorb terrestrial radiation in the wavelength range from 5

to 100 µm. Therefore, the interaction of clouds with radiation needs to be investigated. Al-

though clouds have been studied for several decades, they still pose many challenges in terms

of their observation and representation in weather and climate models (Shonk et al., 2011).

The latest report of the Intergovernmental Panel on Climate Change (IPCC, 2013) classifies

cloud effects as one of the largest uncertainties in climate simulations, significantly contribut-

ing to uncertainties in the determination of the Earth’s energy budget (Stocker et al., 2013).

The large uncertainties arise from an insufficient representation of complex cloud structures

(cloud inhomogeneities) and from cloud-radiation feedback processes that control the cloud

evolution (Stephens, 2005; Shonk et al., 2011). Therefore, the representation of cloud inho-

mogeneities needs to be addressed (Shonk et al., 2011), as changing cloud properties have

an important effect on the interaction of clouds with radiation (Slingo, 1990).

Serious limitations in the quantification of cloud optical properties such as the cloud optical

thickness (τ) exist. High ice clouds (cirrus) and Arctic stratus reveal significant horizontal

inhomogeneities of different origin and horizontal scale. Both cloud types can either warm

or cool the climate system, depending on their optical and microphysical properties and the

meteorological conditions. For example, Choi and Ho (2006) reported for tropical regions

a warming net radiative effect of cirrus with a cirrus optical thickness (τci) of less than 10,

but a cooling effect for τci > 10. For Arctic stratus, Wendisch et al. (2013) showed that for

low surface albedo (αsurf) and low solar zenith angle (θ0), the cloud cools the sub-cloud layer.

With increasing αsurf and increasing θ0, the net cooling effect of the low–level cloud turns

into a net warming (for αsurf(θ0 = 80) > 0.15, αsurf(θ0 = 60) > 0.7, for a low–level cloud

with an optical thickness of τst = 10 in a subarctic summer atmosphere). Thus, the radiative

forcing of cirrus and Arctic stratus depends significantly on the cloud optical thickness and

the surface albedo.

1.1 The Advantage of High Spatial Resolution

Clouds exhibit significant horizontal and vertical inhomogeneity. However, in most cli-

mate simulations and remote-sensing applications they are assumed as plane-parallel with

homogeneous (fixed) particle size and shape (Francis et al., 1998; Iwabuchi and Hayasaka,

2002; Garrett et al., 2003). It is well-known that the traditional use of plane-parallel and

2 1. Motivation and Objectives

homogeneous clouds introduces biases into the modeled radiation budget (Shonk et al.,

2011). Several studies investigated the influence of a plane-parallel assumption on cloud

retrievals (e.g. Cahalan, 1994; Loeb and Davies, 1996; Marshak et al., 1998; Zinner et al.,

2006; Varnai and Marshak, 2007). They found that the model biases are related to the de-

gree of horizontal photon transport, which is ignored in radiative transfer schemes used in

general circulation models (GCM). Multiple scattering due to three-dimensional (3D) mi-

crophysical cloud structures smooth the sampled radiation field. On small scales, this limits

the accuracy of the independent pixel approximations (IPA) results. Cahalan (1994) and

Marshak et al. (1995) revealed discrepancies for individual pixel radiances exceeding 50%.

For the top-of-atmosphere cloud radiative forcing (solar and terrestrial), Shonk and Hogan

(2008) reported an overestimation of about 8%.

3D Monte Carlo radiative transfer simulations account for the horizontal photon transport.

However, they are costly in terms of computer time and memory (Huang and Liu, 2014). This

renders Monte Carlo radiative transfer simulations as inappropriate for the application in op-

erational or global models. Other approaches introduce cloud overlap schemes (COS), such

as the maximum-random COS (Geleyn and Hollingsworth, 1979), the exponential-random

COS (Hogan and Illingworth, 2000), or Triplecloud COS (Shonk and Hogan, 2008). Im-

provements compared to the use of plane-parallel homogeneous clouds were achieved, but

results are still not as accurate as those derived by Monte Carlo simulations or measure-

ments with high spatial resolution. Thus, since many cloud processes occur on small hori-

zontal scales (e.g. cloud particle formation, turbulence), the uncertainties inherent in one-

dimensional (1D) simulations still have to be improved. Therefore, Huang and Liu (2014)

introduced an approach, which uses spatial auto-correlation functions of cloud extinction

coefficients to physically capture the net effects of subgrid cloud interactions with radiation.

With several orders less computational time, this approach is able to reproduce 3D Monte

Carlo radiative transfer simulations with sufficient accuracy. However, the method requires

spatial auto-correlation functions of cloud extinction coefficients with high spatial resolution,

which substantiates the need for measurements of comparable resolution.

GCM or numerical weather forecast models such as that from the European Centre for

Medium-Range Weather Forecasts (ECMWF) require sub-grid scale parameterizations of

e.g. cloud structures, liquid water content (LWC), and/or ice water content (IWC) dis-

tributions (Huang and Liu, 2014). Cloud structures including inhomogeneities show spatial

features down to distances below the meter scale. Therefore, measurements with high spatial

and temporal resolution have to be applied to obtain the parameterizations. The required

measurements include cloud altitude (temperature), its geometry (vertical and horizontal

extent), and cloud microphysical properties (e.g. LWC, IWC, droplet size, ice crystal size

and shape distributions).

As proposed by Marshak et al. (1995), Oreopoulos et al. (2000), or Schroeder (2004),

horizontal cloud inhomogeneities are usually investigated by scale analysis of cloud-top-

reflectances. However, radiance measurements include the information of the scattering

phase function, imprinted in the measured radiance field. To avoid artifacts in the scale

analysis resulting from such features, parameters that account for them (e.g. τ) have to be

analyzed.

1.2. Observation of Cloud Inhomogenieties by Remote Sensing 3

1.2 Observation of Cloud Inhomogenieties by Remote Sensing

The necessary cloud parameters to investigate cloud inhomogeneities and to validate/improve

models can be obtained by in situ measurements or by remote–sensing. In situ measure-

ments benefit from high spatial and temporal resolution, but are restricted to small parts

of the cloud only. Satellite–based remote–sensing covers large horizontal areas but often

does not have sufficient vertical and horizontal resolution (Tab. 1.1); e.g. operational im-

agers, such as the Moderate-Resolution Imaging Spectroradiometer (MODIS, 250-1000m,

King et al., 2003) or the Advanced Very High Resolution Radiometers (AVHRR, 1 km res-

olution, Cracknell, 1997). Horizontal cloud structures smaller than the resolution cannot be

resolved. An improvement of this situation is achieved by coupling satellite observations with

ground–based/airborne in situ/remote–sensing measurements with increased temporal and

spatial resolution. This combination is suitable to validate satellite products and to improve

parameterizations, including cloud-radiative effects generated from horizontal cloud inho-

mogeneities. Frequently applied instruments for such applications are nadir-viewing point

spectrometers such as the Solar Spectral FluxRadiometers (SSFR, Pilewskie et al., 2003) or

the Spectral Modular Airborne Radiation measurement sysTem (SMART, Wendisch et al.,

2001). These instruments provide radiation measurements with high spatial resolution (along

track) within a field of view (FOV) of < 2. Pointing spectrometers are supplemented

by imaging spectrometers with usually lower spectral resolution. They usually measure

in a FOV larger than 30. Examples of imaging spectrometers are the Compact Airborne

Spectrographic Imager (CASI, Anger et al., 1994), the spectrometer of the Munich Aerosol

Cloud Scanner (specMACS, Ewald et al., 2015) or the imaging spectrometer AisaEAGLE

applied for the current thesis.

Table 1.1: Category of remote-sensing techniques, instruments, and spatial resolution/coverage. Thespectral instrumental characteristics are indicated by index B (bands) and M (multi-spectral).

Category Instruments Pixel Size (m) Coverage

Imaging Spectrometer CASIM, specMACSM, AisaEAGLEM < 15 LocalPoint Spectrometer SSFRM, SMARTM < 100 LocalOperational Imager MODISB, AVHRRB 250-1000 Global

Figure 1.1 illustrates a cloud as observed from above with different spatial resolutions. It

shows the advantage of high resolving imaging spectrometers (Fig. 1.1a) compared to nadir-

viewing point spectrometers (Fig. 1.1b) and to operational imagers carried by satellites

(Fig. 1.1c and d). Detailed investigations of horizontal cloud inhomogeneities are not feasible

from MODIS and AVHRR measurements. From Fig. 1.1b, cloud structures are derived with

high spatial resolution along track of the measurements, but due to the small FOV, 2D dis-

tributions of cloud structures are not represented adequately. From imaging spectrometers

(Fig. 1.1a), both high spatial resolution and large 2D coverage of the investigated cloud can

be resolved. Thus, imaging spectrometers are very useful to investigate small-scale cloud in-

homogeneities over large areas. For example, using airborne remote-sensing spectral imaging

sensors during the international field campaign SoRPIC (Solar Radiation and Phase dis-


Figure 1.1: Radiance at 645 nm wavelength of a cloud scene, as observed with different ground-pixelsize resolution of (a) 5m (CASI, specMACS, AisaEAGLE), (b) 50m (SSFR, SMART), (c) 250m(MODIS), and (d) 1 km (MODIS, AVHRR).

crimination of ArctIc Clouds), Bierwirth et al. (2013) showed that τ can be retrieved with

a spatial resolution below 5m. An even larger FOV can be achieved with commercial digital

cameras (Ehrlich et al., 2012). However, they mostly provide measurements in three spectral

wavelength bands only (red, green, blue; RGB). Therefore, they lack of necessary spectral

resolution, which is needed to retrieve cloud parameters such as τ or reff.

1.3 Complications of Retrievals of Cirrus Properties

Satellite-based cirrus cloud climatology such as reported by Sassen and Campbell (2001),

Sassen and Benson (2001), and Sassen and Comstock (2001) include cloud cover, cirrus op-

tical thickness and crystal effective radius. Each change in one of those parameters modifies

the magnitude of their radiative forcing. For example, current global circulation models

assume a standard value of 25 µm for the ice crystal effective radius. For slightly smaller

crystals, the cirrus would have a stronger cooling effect (Garrett et al., 2003). Furthermore,

cirrus often shows spatial and temporal variability and is optically thin. This complicates

the detection of cirrus by common remote-sensing techniques. The applicability of remote-

sensing data is limited by 3D radiative effects, but also by the number of wavelength bands

and spatial resolution of the sensors. Numerous studies investigated cirrus radiative-effects

1.3. Complications of Retrievals of Cirrus Properties 5

from satellite and ground–based observations as well as by means of numerical simulations

(Liou, 1986; Lynch et al., 2002; Yang et al., 2007; Baran, 2012).

For optical thickness retrieval, the microphysical composition of the cloud (non-spherical ice

crystals) adds a crucial complication. The representation of the scattering properties of cloud

droplets is well known and is described by Mie-Theory (Mie, 1908; Bohren and Huffman,

1998). However, optical properties of ice crystals such as the extinction coefficient, scat-

tering phase function, and single–scattering albedo differ significantly from those of liquid

water droplets (Takano and Liou, 1989; Fu and Liou, 1993; Macke, 1993). The crystal shape

can change the cloud radiative properties substantially, which may cause biases in satel-

lite retrievals (based on reflected radiance, Eichler et al., 2009) and radiative energy budget

estimates (related to irradiance, Wendisch et al., 2005, 2007). For the retrieval of τci as-

sumptions about the crystal shape and the corresponding scattering properties are made.

However, the ice crystal shape is an important parameter influencing the radiative proper-

ties of ice clouds (e.g., Macke et al., 1998; Wendisch et al., 2005, 2007; Eichler et al., 2009).

Eichler et al. (2009) showed that these assumptions can add an uncertainty of up to 70%

and 20% in retrievals of τ and reff, respectively. With regard to cirrus solar radiative forcing,

Wendisch et al. (2005) revealed uncertainties of up to 26%. Progress in the parameterization

of optical properties of ice crystals in GCM has been made (e.g., Kristjansson et al., 2000;

Edwards et al., 2007) using an ensemble of ice crystal shapes including roughened surfaces.

Recent studies by Baum et al. (2005a,b, 2007); Yang et al. (2005, 2012) and Yi et al. (2013)

emphasize the parameterization of ice particle surface roughness, which results in a reduction

of the asymmetry factor compared to smooth particles of the same size. Although progress

is reported, difficulties in retrievals of cirrus properties are still significant, especially for

optically thin cirrus (Comstock et al., 2007).

A method to determine the ice crystal shape was proposed by Chepfer et al. (2002). It is

based on multiangle satellite measurements of cloud-top-reflectance and polarized bidirec-

tional radiances in the visible wavelength range (Chepfer et al., 2001). Another method,

based on imaging spectrometry was proposed by McFarlane and Marchand (2008). They

developed a best-fit ice crystal scattering model that uses angular dependent measure-

ments from coincident Multi-angle Imaging SpectroRadiometer (MISR) and MODIS re-

flectances. Sensitivity to particle shape is provided by the multi-angle information from

MISR. McFarlane and Marchand (2008) were able to distinguish between ice crystal habits

such as aggregates and plates.

To check the cirrus retrieval algorithms airborne versions of spectroradiometers above cirrus

are applied, such as the MODIS Airborne Simulator (MAS). With extensive microphysi-

cal and solar radiation instruments as well as radiative transfer simulations, Schmidt et al.

(2007) and Eichler et al. (2009) investigated the differences between retrieved and measured

microphysical cloud properties. Schmidt et al. (2007) revealed gaps between the retrieved ef-

fective radius from MAS and simultaneous in situ measurements. This disagreement has not

been resolved yet, partly because it has been difficult to collocate remote sensing above the

clouds and concurrent in-cloud microphysical measurements. However, such observations are

important to link satellite cloud observations of coarse resolution to spatially highly resolved

measurements of cloud properties. Such experiments are rare, partly because instruments like


MAS are complex and expensive and are not available for frequent cloud observations. How-

ever, progress in performing collocated in situ and radiation measurements is reported. For

example, Werner et al. (2014) successfully investigated shallow cumuli from collocated micro-

physical and remote-sensing measurements using helicopter-towed measurement platforms.

Furthermore, Finger et al. (2015) introduced a measurement technique (related to spectral

optical layer properties), based on an aircraft-towed measurement platform. Such towed

platforms can also be used to validate satellite retrievals of coarse resolution. Finger et al.

(2015) showed that such measurements are complex. The high flight speed requires a rope

of several kilometers length to allocate the measurement platform a few hundred meter be-

low the aircraft. As an alternative, measurements with ground-based imaging spectrometers

provide information on cirrus inhomogeneities in terms of radiance, cirrus optical thickness,

and cirrus crystal shape.

1.4 Current Limitations for Arctic Stratus Cloud Retrieval

Sea ice is characterized by a heterogeneous horizontal distribution. It has irregular surfaces

and is usually broken into pieces, called floes (Rothrock and Thorndike, 1984). Openings in

the ice surface (cracks, leads, and polynias) are common especially in the transition zone

between sea ice and open water, accompanied by fields of scattered ice floes. The surface

albedo contrast in such areas is extreme and partly occurs on small horizontal scales in

a range of less than tenth of meters. For visible wavelengths the surface albedo of open water

is low (0.042 at 645 nm; Bowker et al., 1985), while that of ice-covered ocean is high (0.91

at 645 nm; Bowker et al., 1985). These differences decrease in the near-infrared wavelength

range (αwater = 0.01 and αsnow = 0.04 at 1.6 µm wavelength; Bowker et al., 1985).

Using AVHRR data from the polar-orbiting satellites NOAA-10 and NOAA-11 (National

Oceanic and Atmospheric Administration), Lindsay and Rothrock (1994) analyzed the

albedo of 145 different 200 km2 cells in the Arctic. The mean values for the cloud-free

surface of individual cells ranged from 0.18 to 0.91 and were highly variable at monthly and

annual time scales. The application of the retrieval by Bierwirth et al. (2013) is restricted to

areas of open water. A variable Arctic surface albedo as quantified by Lindsay and Rothrock

(1994) complicates the retrieval of cloud microphysical and optical properties using only

visible wavelengths (Platnick, 2001; Platnick et al., 2004, 2003; Krijger et al., 2011). To

overcome this limitation, near-infrared channels are used in addition in the retrieval algo-

rithms. For MODIS the 1.6 µm band reflectance is applied as a surrogate for the traditional

non-absorbing band in conjunction with a stronger absorbing 2.1 or 3.7µm band (Platnick,

2001; Platnick et al., 2004, 2003). However, an accurate separation between sea ice and

open water needs to be performed before the retrieval algorithms are applied. Operational

algorithms (e.g. for MODIS), use NOAA’s microwave-derived daily 0.25 Near Real-Time

Ice and Snow Extent (NISE; Armstrong and Vazquez-Cuervo, 2001; Platnick et al., 2003)

to identify snow- or ice-covered scenes. For the typical scale of ice floes this pixel size is not

sufficient.

Even when ice and ice-free areas are perfectly separated, 3D radiative effects can af-

fect the cloud retrieval over ice-free pixels close to the ice edge. Lyapustin (2001) and

1.5. Objectives 7

Lyapustin and Kaufman (2001) quantified the impact of the contrast of the surface albedo

between open sea and adjacent sea-ice or snow on the retrieval of Arctic cloud properties.

Adjacency effects are found to reduce the apparent surface contrast by decreasing the top-of-

the-atmosphere reflectivity γλ over bright pixels and increasing the brightness of dark pixels,

which becomes important for land remote-sensing applications developed for usage with both

dark or bright targets.

Surface 3D radiative effects interfere with cloud 3D radiative effects due to cloud inhomo-

geneities. In the case of Arctic stratus, the individual cloud 3D effects are of minor impor-

tance. For a solar zenith angle θ0=45, Zinner et al. (2010) found that the remote-sensing

of stratocumulus was not biased by 3D effects, while that of scattered cumulus was sensitive

to horizontal heterogeneities. This leads to the assumption that retrievals of cloud micro-

physical and optical properties can be treated by 1D simulations if the distance to ice-open

water boundaries is sufficiently large. However, measurements in Arctic regions are mostly

performed for solar zenith angles larger than 45. In such cases, 3D radiative effects gen-

erated by the cloud structures become important. Using plane-parallel 1D simulations of

clouds, Loeb and Davies (1996) stated that τ shows a systematic shift towards larger values

with increasing θ0. This dependence is weak (≤ 10%) for thin clouds (τ ≤ 6) and θ0 ≤ 63.

Grosvenor and Wood (2014) confirmed this statement. They investigated MODIS satellite

retrieval biases of τ and reported that τ is almost constant between θ0=50 and θ0 ≈ 65–70,

but then increases rapidly by over 70% between the lowest and highest θ0.

Jakel et al. (2013) quantified the effect of local surface-albedo heterogeneity and aerosol pa-

rameters on the retrieved area-averaged surface albedo from airborne upward and downward

irradiance measurements. For adjacent land and sea, Jakel et al. (2013) defined a critical

distance at which the retrieved area-averaged surface albedo deviates by 10% from the given

local surface albedo. It was found that this critical distance ranges in the order of 2.4 km for

a flight altitude of 2 km and is larger for albedo fields with higher surface albedo contrast. In

the case of clouds with an optical thickness larger than that of aerosol particles, this effect

is expected to increase significantly.

1.5 Objectives

In the following chapters the development and application of new cloud retrieval methods

based on imaging spectrometer measurements from the ground and using airborne carriers

is introduced. The potential of imaging spectrometers in remote–sensing applications is

evaluated and demonstrated by two applications. The analyzed data are obtained from

imaging spectrometer measurements in the visible wavelength range (400–970 nm) with high

spatial (< 10m) resolution (AisaEAGLE, Hanus et al., 2008; Schafer et al., 2013, 2015). The

data were collected during the two international field campaigns Clouds, Aerosol, Radiation,

and tuRbulence in the trade wInd regime over BArbados (CARRIBA) on Barbados in April

2011, and VERtical Distribution of Ice in Arctic clouds (VERDI) in Inuvik, Canada in

May 2012.


The data are used to retrieve fields of highly resolved cloud optical thickness to investigate

the horizontal distribution of cloud inhomogeneities. Two different configurations have been

applied to derive the fields of τ :

For CARRIBA, ground-based measured downward solar radiance transmitted through

cirrus, and

For VERDI, airborne measured upward solar radiance reflected by Arctic stratus.

The investigation of the retrieved fields of τ with regard to the horizontal distribution of

cloud inhomogeneities is performed by:

A statistical evaluation using common inhomogeneity parameters, and

A characterization of the spatial distribution using auto–correlation functions and

power spectral density analysis.

Chapter 2 introduces the terminology applied in this thesis. In Chapter 3 the applied in-

strument (AisaEAGLE) is characterized. Its calibration and data evaluation procedures are

described and exemplified. Chapter 4 introduces a new method to retrieve the cirrus optical

thickness from spectral radiance data, which uses angular sampling of the phase function

to obtain information about the particle shape. In Chapter 5, airborne observations of the

spectral reflectivity of Arctic stratus are presented. A robust algorithm separating sea-ice

and open-water surfaces under cloud cover is introduced and applied to the measurements.

Observations and simulations of the 3D radiative effects are investigated with regard to their

influence on 1D retrievals of τ and reff. In Chapter 6, the derived fields of τ are investigated

regarding their inhomogeneity. Conclusions and an outlook are given in Chapter 7.

9

2 Definitions

This chapter introduces the nomenclature applied in this thesis. It introduces general ra-

diometric quantities (Sect. 2.1) and cloud optical properties (Sect. 2.2). In Sect. 2.3 the

radiative transfer equation (RTE) is described and in Sect. 2.4 the cloud microphysical prop-

erties. The definitions follow the textbooks of Bohren and Clothiaux (2006), Petty (2006),

and Wendisch and Yang (2012).

2.1 Radiative Quantities

The spectral radiant energy flux Φλ characterizes the radiant energy Erad that passes through

an infinitesimal area element d2A within a given time interval t+dt for a selected wavelength

range λ+ dλ. Therefore, Φλ is defined by:

Φλ =d2Erad

dtdλ. (2.1)

Φλ(t) carries the units J s−1 nm−1. It defines the power of radiant energy at a given time t.

Φλ(t) can be expressed in the unit of Wnm−1. Normalizing Φλ to the corresponding area

element d2A results in the spectral radiant energy flux density Fλ:

Fλ =d2Φλ

d2A=

d4Erad

d2Adt dλ. (2.2)

Fλ is also called spectral irradiance and is given in units of Wm−2 nm−1. Fλ describes

the spectral radiant energy flux, which passes trough an unit area from all directions of

a hemisphere. For atmospheric applications, the area element d2A is considered horizontal;

the orientation of the unit vector is perpendicular to d2A and points in zenith direction.

Pointing into the direction of propagation s, Erad within a solid angle element d2Ω is quan-

tified by the spectral radiance Iλ(s):

Iλ(s) =d4Φλ

cos θ d2Ad2Ω=

d6Erad

dt dλ cos θ d2Ad2Ω. (2.3)

The unit of Iλ(s) is Wm−2 nm−1 sr−1. With regard to the position of the Sun and the

direction s, the radiance is defined as upward I↑λ(s) or downward I↓λ(s). Figure 2.1 illustrates

the geometry for the definition of Iλ(s).

In Fig. 2.1, the definition of a solid angle element d2Ω is used (solid angle is related to

regular angle as area is related to length), which can be described with the directional angles

10 2. Definitions

Figure 2.1: Illustration of the definition of radiances using a solid angle element described by thezenith angle θ and azimuth angle φ.

θ (zenith angle) and φ (azimuth angle). The area on the sphere marked by the depicted

sector in Fig. 2.1 is defined by:

d2A⊥ = r2 · sin θ dθ dφ. (2.4)

Using this equation and following the definition of a solid angle, the solid-angle element

illustrated by the pyramid in Fig. 2.1 and observed from the origin of the coordinate system

is given by:

d2Ω =d2A⊥r2

= sin θ dθ dφ. (2.5)

The solid-angle element d2Ω is given in units of sr (steradian). In the next step, a projection

of d2A onto the perpendicular plane with regard to the direction of propagation s is necessary:

d2A⊥ = cos θ · d2A. (2.6)

Fλ can be derived by integrating Iλ(s) over all angles within a hemisphere:

Fλ =

∫∫2π

Iλ(s) · cos θ d2Ω =

∫ 2π

0

∫ π

0Iλ(θ, φ) · cos θ · sin θ dθ dφ. (2.7)

Assuming an anisotropic radiation field, the downward irradiance F ↓λ is composed of a direct

and diffuse component, whereas the upward irradiance F ↑λ consists of a diffuse component

only. Contrarily, assuming an isotropic radiation field, the radiance is independent of the

orientation of s. In this case, the following relation can be derived:

Fλ = π sr · Iλ. (2.8)

2.2. Cloud Optical Properties 11

The spectral cloud albedo ρλ and spectral surface albedo αλ are derived from the ratio of

upward and downward spectral irradiance. Here, the spectral cloud albedo is related to the

particular cloud top (ct), whereas the spectral surface albedo is related to the current surface

level (surf).

ρλ(zct) =F ↑λ (zct)

F ↓λ (zct)

(2.9)

αλ(zsurf) =F ↑λ (zsurf)

F ↓λ (zsurf)

. (2.10)

Due to conservation of energy, the particular range of ρλ(zct) and αλ(zsurf) is limited to

values between 0 and 1.

The spectral reflectivity γλ can be derived from the quantities Fλ and Iλ(s). With regard

to clouds, the spectral reflectivity γλ is related to the cloud top altitude zct. It is defined by

the following equation:

γλ(zct) =I↑λ(θ = π, zct)

F ↓λ (zct)

· π sr. (2.11)

In contrast to the spectral albedo (ρλ, αλ), γλ(zct) can have values larger than 1. However, in

case of an isotropic radiation field, γλ(zct) yields the same value as ρλ(zct), compare Eq. (2.8).

2.2 Cloud Optical Properties

On its way from the top of atmosphere to the surface, solar radiation is scattered, absorbed

and emitted by individual particles such as gas molecules, aerosol and cloud particles. To

characterize such processes, single-scattering properties are defined (extinction cross sec-

tion Cext, single–scattering albedo ω, and scattering phase function P).

Liquid water droplets are spherical and Mie–theory yields analytic expressions for these

quantities (Mie, 1908; Bohren and Huffman, 1998). The single–scattering properties of non–

spherical particles (ice crystals and aerosol particles) cannot be described by an analytic

solution and numerical methods have to be applied. Spectral single–scattering properties of

different ice crystal shapes and sizes are published e.g. by Baum et al. (2005a,b), Yang et al.

(2005), Baum et al. (2007).

2.2.1 Extinction Cross Section

Individual particles attenuate incident electromagnetic radiation, which is quantified by the

extinction cross section Cext (a function of the mass to cross–sectional area). It is defined

by:

Cext =Φext

Finc. (2.12)

12 2. Definitions

Cext represents the extinguished radiant energy flux (Φext) divided by the incident radiative

flux density Finc. The extinguished part of the solar radiation is composed of the scattered

and absorbed part of the electromagnetic wave. Thus, the extinction cross section Cext can

also be derived by the sum of the scattering cross section Csca and the absorption cross

section Cabs:

Cext = Csca + Cabs =Φsca + Φabs

Finc. (2.13)

Cabs defines the probability of absorption and is related to the imaginary part of the refractive

index. It is given in units of m2.

2.2.2 Single–Scattering Albedo

The particles single–scattering albedo ω describes the ratio between the scattering and ex-

tinction of electromagnetic radiation. Therefore, it is a mass for the absorbed part of elec-

tromagnetic radiation. It is a dimensionless value related to the spectral complex index of

refraction. The particle single–scattering albedo is defined by:

ω =Csca

Csca + Cabs. (2.14)

The magnitude of ω ranges between 0 (full absorption, no scattering) and 1 (no absorption,

only scattering). As for Cabs, ω defines the probability of absorption and is related to the

imaginary part of the refractive index ni (due to the dependence on Cabs).

In the visible and near infrared wavelength range below 1000 nm, liquid water droplets show

no significant absorption features. Here, ω yields values almost equal to 1. Beginning at

1500 nm wavelength, liquid water shows increased absorption (decreased ω). An additional

feature at the near infrared wavelength range above 1000 nm is the dependence of ω on the

cloud droplet size. ω decreases with increasing droplet size. Contrarily, this dependence is

negligibly small at wavelengths below 1000 nm.

2.2.3 Scattering Phase Function

Solar radiation is scattered into different directions. The scattering phase function P(ϑ, φ),

which is a function of the particles shape, size and orientation, defines the angular probability

distribution of the scattered radiation. With regard to µ as the cosine of the solar zenith

angle (µ0 = cos θ0), it is given as a function of the direction of the incident solar radiation

(µ′, φ′) to all scattering directions (µ, φ). Thus, the scattering phase function P(ϑ, φ), which

is normalized to 4π, is given by:∫ 2π

0

∫ 1

−1P([µ′, φ′], [µ, φ]) dµ dφ = 4π sr. (2.15)

2.2. Cloud Optical Properties 13

If the ice crystals are randomly oriented, or azimuthal averaging is performed, the magnitude

of P reduces to the relation between the incident and scattered direction regarding the

observed cross section (scattering plane). Using this relation, given by the scattering angle ϑ:

cosϑ = µ · µ′ +√

1− µ2 ·√

1− µ′2, (2.16)

the scattering phase function is expressed as P(cosϑ). Figure 2.2 illustrates P(ϑ) for a single

cloud droplet and ice crystals of different shapes.

Figure 2.2: Scattering phase function P(ϑ) as a function of scattering angles ϑ for a normal distri-bution of cloud droplets with average diameter of 20µm± 2 µm and ice crystals (solid column, plate,droxtal, aggregate), each with a maximum diameter of 20 µm at 530 nm wavelength. The P(ϑ) of icecrystals and cloud droplets are derived from a data base of scattering features, based on the code by(Yang et al., 2013).

Due to the varying size and shape of the selected cloud particles, the illustrated P(ϑ) show

significant differences. P(ϑ) for ice crystals is smoother than P(ϑ) for water droplets. This

is a result of the randomly orientation of the ice crystals and/ or the azimuthal averaging of

the ice crystals P(ϑ, φ). P(ϑ) of liquid water droplets shows fluctuations, the P(ϑ) of the

various ice crystals do not. This results from resonances in the solution of the Mie-Theory.

Furthermore, the forward scattering peak of liquid water droplets is reduced. Contrarily,

the P(ϑ) of ice crystals exhibit a strong but narrow forward scattering peak near ϑ=0.

In the range of the sideward scattering, P(ϑ) of liquid water droplets is characteristically

lower than that of ice crystals. Further, the P(ϑ) of the ice crystals show the characteristic

halo structures at ϑ=22 and ϑ=46, while the cloud droplets show the typical cloud

bow at ϑ≈ 140. Plates and solid columns (hexagonal ground area) exhibit the strongest

forward scattering peak, while P(ϑ) of aggregates shows the smoothest shape due to random

orientation.

14 2. Definitions

2.2.4 Cloud Optical Thickness

The cloud optical thickness τ is a volumetric cloud property. Volumetric cloud properties

are derived by integrating over the single scattering properties, weighted by the number-size

distribution dN/dD(D) with the particle number concentration N of the cloud particles with

diameter D (Wendisch et al., 2005).

The cloud optical thickness τ is derived via integration over the spectral volumetric extinction

coefficient bext of a total cloud column from the cloud base zbase to the cloud top ztop:

τ =

∫ ztop

zbase

bext(z′) dz′. (2.17)

bext in the unit of m−1 is defined as follows:

bext =

∫Cext ·

dN

dD′ (D′) dD′. (2.18)

2.3 Radiative Transfer Equation

The Radiative Transfer Equation (RTE) describes the propagation of electromagnetic radi-

ation in the atmosphere taking absorption, emission, and scattering processes into account.

The RTE is determined by the spectral volumetric extinction coefficient bext, single–scattering

albedo ω, and scattering phase function P.

Starting from the law of Beer, Lambert and Bouguer the attenuation of direct solar radiance

Iλ,dir(τ, µ0, φ0) along a path through the atmosphere is characterized by:

Iλ,dir(τ, µ0, φ0) =S0

4π sr· exp

(− τ

µ0

), (2.19)

S0 represents the extraterrestrial irradiance at the top of the atmosphere. It is attenuated

exponentially along its path through the atmosphere. Considering a solar zenith angle of 30

and a cloud with an optical thickness of τ = 10, the transmitted fraction of the direct solar

radiance through the cloud is in the range of about 0.1%. Thus, radiative transfer processes

through clouds can only be described taking additionally into account the diffuse part of the

solar radiance Iλ,diff . Originally introduced by Chandrasekhar (1950), the 1D RTE is given

by:

µdIλ,diff(τ, µ, φ)

dτ= Iλ,diff − (Jλ,dir + Jλ,diff). (2.20)

It is valid for plane–parallel and horizontally homogeneous atmospheric conditions. The

direction of propagation of Iλ,diff is given by µ and φ. The radiation scattered into the

viewing direction is characterized by two source terms: a single scattering term Jλ,dir and

2.4. Cloud Microphysical Properties 15

a multiple scattering term Jλ,diff . Jλ,dir specifies the direct radiation, while Jλ,diff specifies

the diffuse radiation. The two terms are given by (Wendisch and Yang, 2012):

Jλ,dir =ω(τ)

4π sr· S0 · exp

(− τ

µ0

)· P(τ, [−µ0, φ0], [µ, φ])

Jλ,diff =ω(τ)

4π sr

∫ 2π

0

∫ 1

−1Iλ,diff(τ, µ

′, φ′) · P(τ, [µ′, φ′], [µ, φ]) dµ′ dφ′.

(2.21)

The incoming solar radiation Jdir is attenuated according to the law of Beer, Lambert and

Bouguer and scattered into the viewing direction. The source terms depend on absorption

(as defined by the single–scattering albedo ω) and scattering (as defined by the scattering

phase function P). Thus, Jdir contains information on the particular ice crystal shape. The

diffuse part Jλ,diff is also related to ω and P, but additionally to the cloud optical thickness τ .

2.4 Cloud Microphysical Properties

The scattering phase function for the liquid cloud droplet illustrated in Fig. 2.2 is related to

cloud droplets with a size of 20 µm. In reality, liquid water clouds consist of wide spectra of

differently sized liquid water droplets. Therefore, the resulting scattering phase function is

related to a number-size distribution. The effective cloud droplet radius reff in units of µm

is defined to quantify an average size of cloud droplet populations. It represents the ratio

of the third (volume) to the second moment (surface area) of the cloud droplet number size

distribution dN/dD(D). Here, D is the geometrical droplet diameter. It characterizes the

mean droplet radius in an ensemble of cloud droplets, weighted by dN/dD(D). The effective

cloud droplet radius reff is given by:

reff =1

2

∫D′3 dN

dD′ (D′) dD′∫D′2 dN

dD′ (D′) dD′. (2.22)

Following Yang et al. (2000) and Key et al. (2002), reff can also be defined for ice crystals. To

derive reff for an ice crystal, its maximum dimension Dmax, its volume VD and its projected

area AD have to be determined. The definition of reff for ice crystals is then given as follows:

reff =3

4

∫VD(D

′) · dNdD′ (D′) dD′∫

AD(D′) · dNdD′ (D′) dD′

. (2.23)

VD and AD are derived from calculating the diameter of a sphere, which consists of the

same volume to surface ratio as the ice particle would have (Grenfell and Warren, 1999;

Yang et al., 2000).

The liquid water content LWC defines the mass of liquid water in a cloud volume of 1m3.

With the density of liquid water ϱw, it is defined as follows:

LWC = ϱw · 43· π ·

∫ (D′

2

)3

· dNdD′ (D

′) dD′, (2.24)

16 2. Definitions

Following Brenguier et al. (2011), the LWC can be described for a vertically homogeneous

cloud at an altitude between zbase and ztop by the use of the prior defined reff and τ :

LWC =2

3·∫ ztop

zbase

reff · τ · ϱwz′

dz′. (2.25)

In reality, vertically homogeneous clouds are exceptional. Commonly, the droplet size in-

creases from the cloud base to the cloud top. Wood and Hartmann (2006) showed that by

using 5/9 instead of 2/3, Eq. (2.25) turns into the relation for such adiabatic clouds. The

definition of the LWC can also be translated to ice clouds. Here, the ice water content IWC

is defined as follows:

IWC = ϱi ·∫

VD(D′) · dN

dD′ (D′) dD′, (2.26)

where ϱi gives the density of an ice crystal with the volume VD.

17

3 Experimental

This chapter characterizes the technical parameters of the imaging spectrometer

AisaEAGLE, which was used for the measurements presented in this thesis. The calibra-

tion procedure, data handling and necessary corrections are introduced in Sect. 3.1.1 to

3.2.6. Details of the observation geometry and the derivation of scattering angles from

AisaEAGLE measurements are provided in Sect. 3.3. Parts of this chapter have been pub-

lished in Schafer et al. (2013, 2015).

3.1 Imaging Spectrometer AisaEAGLE

3.1.1 Specifications

The AisaEAGLE is a commercial imaging spectrometer, which is manufactured by Specim

Ltd. in Finland (technical specifications summarized in Tab. 3.1, Hanus et al., 2008;

Schafer et al., 2013). It is an analytically detection and mapping instrument, originally

designed for airborne applications. AisaEAGLE has been applied in various fields including

forestry management, environmental investigations, target identification, water assessment,

and land use planning.

The AisaEAGLE is a single-line sensor with 1024 spatial pixels. The instrument measures

radiances in three dimensions: space, time and wavelength. The spatial and spectral dimen-

sions are resolved by an optical assembly that displays the image onto a two-dimensional (2D)

sensor chip. The third dimension, time, corresponds to the motion of the scene, which passes

the sensor. An optical schematic for the path of the electromagnetic radiation detected by

the AisaEAGLE is shown in Fig. 3.1.

The incoming solar radiation within the FOV of AisaEAGLE is collected by a lens and

an entrance slit. Collimating optics direct the radiation to a grating (dispersing element),

where it is dispersed into its spectral components. The spectral components are focused on

the detector, which consists of a charge-coupled device (CCD) element for the spatial and

spectral dimensions.

AisaEAGLE is applied to ground-based and airborne measurements. For airborne measure-

ments (e.g., Bierwirth et al., 2013; Schafer et al., 2015), the 2D image evolves from the sensor

movement. During ground-based applications, the 2D image evolves from the cloud move-

ment across the sensor line (Schafer et al., 2013). If the sensor is aligned perpendicular to

the heading of the aircraft or the direction of the cloud movement, 2D images of clouds with

high spatial resolution (1024 spatial pixels within 37 FOV) are obtained. The FOV of the

18 3. Experimental

Figure 3.1: Optical scheme of an imaging spectrometer.

AisaEAGLE and the detected swath of the measured scene depends on the lens that is used

for the measurements. The measurements presented in the following were performed with

a 36.7 lens (18.09mm focal length) and a 36.3 lens (18.30mm focal length). Figure 3.2

shows the size of a single image pixel and the swath of the entire image as a function of the

distance to the target for the 36.7 lens.

Figure 3.2: Characteristic (a) swath and (b) pixel width for AisaEAGLE using the 36.7 lens.

The swath s of a detected scene at a distance of ∆z is derived by:

s = 2 · tan(1

2FOV

)·∆z. (3.1)

The opening angle of each spatial pixel FOVpix is obtained by the total FOV and the total

number of spatial pixels npix.

FOVpix =FOV

npix(3.2)

3.1. Imaging Spectrometer AisaEAGLE 19

The width of each spatial pixel spix is obtained from the combination of Eqs. (3.1) and (3.2),

which leads to:

spix = [tan(npix · FOVpix)− tan((npix − 1) · FOVpix)] ·∆z, npix = −512, ...,−1, 1, ..., 512

(3.3)

While the swath increases with distance to the cloud by the tangent of the opening angle, the

pixel size depends on its position on the sensor line. The FOV of a pixel (the pixel width)

in the center (viewing zenith) is smaller than that of a pixel at the edge. For example,

a cloud at an altitude of 10 km yields an average pixel size of 6.6m (6.3m–6.9m) with

6.7 km swath. To obtain 2D images, the temporal dimension of the spectral measurements

translates to a spatial quantity: the length lpix of the FOV of a pixel is the product of the

perpendicular cloud drifting velocity vcloud (ground-based application) or the aircraft speed

vaircraft (airborne application) and the selected integration time tint for the measurement.

Accounting for a non-perfect perpendicular orientation with the angle α between the flow

direction of the cloud or heading of the aircraft and the orientation of the sensor line, lpix is

given by:

lpix = |sin α| · vcloud, aircraft · tint. (3.4)

The AisaEAGLE CCD element consists of 1024 spectral pixels for the hypothetic wavelength

range from 100 to 1300 nm. However, due to the optical assembly, the effective spectral range

of AisaEAGLE is decreased to 488 pixels (npix=279–766) in the range of 400 to 970 nm

(effective wavelength range). Spectral pixels below or above this range receive stray light

from pixels within the effective wavelength range. This makes those pixels useless for data

evaluation.

Since the spectral range of AisaEAGLE covers more than one octave, the range from 800–

970 nm requires order sorting. This results from the spectrometer technique that is based on

a transmission diffraction grating where the different wavelengths are diffracted to angle β

according to the grating equation:

M · λ = d(sinα+ sinβ), (3.5)

Here, M is the diffraction order (0, ±1, ±2, ...), λ is the wavelength, d is the groove spacing

and α is the angle between incoming radiation and the grating. There is more than one

wavelength that satisfies this equation for a particular set of α and β. In practice, this

means that there are overlapping orders of spectra that go to the same place on the detector

surface. To avoid this, AisaEAGLE has a second order depression using order blocking filters

mounted near the detector.

Applying the full spatial and spectral (1.25 nm full width at half maximum, FWHM) resolu-

tion to the AisaEAGLE measurements, the frame rate (frames per second, FPS) is adjustable

from 4 to 30Hz, while for ground-based applications 4 to 10Hz and for airborne applications

20 to 30Hz were found to be sufficient. Depending on the frame rate, the integration time

is adjustable between 0.1 and 200ms; it is chosen with regard to the particular illumination

of the scene to avoid a saturation of the sensor pixels.

20 3. Experimental

3.1.2 Binning

The AisaEAGLE produces vast amounts of data. A rough approximation arrives at 75GB

of data per hour. This value can be reduced by lowering the spectral and/or the spatial

resolution, so–called binning. Furthermore, this leads to an increased possible recording

speed because pixels are physically joined in read–out, which reduces the process steps to

read an image frame from the sensor. It is also possible to reduce the spectral range or

resolution using band files, but that does not affect the recording speed as it does not reduce

the amount of physical read-out steps. Figure 3.3 illustrates the binning procedure for spatial

and spectral binning and a combination of both. The number of spatial pixels and spectral

bands depends on the applied binning; e.g. a 2x2 binning results in 512 spatial pixels and

244 spectral bands. Accordingly, Eq. (3.2) and Eq. (3.3) have to be adjusted. The available

FWHM, frame rate and number of spectral bands for the different binning configurations

are listed in Tab. 3.1.

Figure 3.3: Scheme of AisaEAGLEs binning procedure for 1x1, 1x2, 2x1, and 2x2 binning.

Because of the increased possible recording speed the instrument allows the usage of higher

frame rates. This is important especially for airborne observations. Due to the high speed

of an aircraft, a too low frame rate causes gaps in the observed scene.

3.2 Calibrations and Data Handling

3.2.1 Radiometric Calibration

AisaEAGLE converts the detected photon counts into digital 12-bit numbers, which results

in 0 to 4096 Analog-Digital-Units (ADU) per integration time. An absolute radiometric

calibration is necessary to transform those numbers (Signal S) into radiances Iλ in units of

3.2. Calibrations and Data Handling 21

Table 3.1: Summarized specifications of the imaging spectrometer AisaEAGLE.

Parameter Specification

Number of spatial pixels 1024Number of spectral bands (total / effective) 1024 / 488Spectral range λ 400–970 nmSpectral resolution (depending on binning) 1.25–9.2 nmTarget resolution at 1000m distance (center pixel) 0.68mSwath width 0.68 · distanceSlit width 30 µmFocal Length 18.5mmFOV 37.7

Image Rate (FPS) 4–160HzSNR (depending on band configuration) 350:1–1400:1Integration Time tint Adjustable to FPSOutput 12 bits digital

Spectral binning options 1–X 2–X 4–X 8–X

Number of spectral bands (effective) 488 244 122 60Spectral resolution (FWHM) 1.25 nm 2.3 nm 4.6 nm 9.2 nmImage rate, up to (FPS) 30Hz 50Hz 100Hz 160Hz

Wm−2 nm−1 sr−1. The manufacturer provides a data sheet with calibration factors. Because

of the fixed mounting of the AisaEAGLE optics within a solid housing, those calibration fac-

tors are supposed to be temporally constant. Nevertheless, this stability is checked using

a radiometric calibration in the laboratory, before and after the AisaEAGLE imaging spec-

trometer is transported to field observations. The radiometric calibration is performed with

an integrating sphere, a certified radiance standard (uncertainty: ± 6%), traceable to the

United States National Institute of Standards and Technology. The calibration setup using

an integrating sphere is illustrated in Fig. 3.4.

The integrating sphere is hollow with a barium sulfate coating on the inner walls. Thus,

the inside of the integrating sphere is assumed to be a Lambertian reflector. The spectral

radiation is emitted into the sphere by a halogen lamp, which is installed at the side of the

sphere and mounted within a ventilated housing. The spectral, diffuse radiation exits the

sphere through an aperture at the front side. It is sampled by the AisaEAGLE inlet, which is

positioned in a distance of about 1 cm in front of the aperture. Due to this distance, a black

fabric is used to prevent from additional radiation, which might enter the optical path from

outside the sphere. Furthermore, a baffle inside the sphere prevents from measuring the

direct, not yet diffuse radiation of the lamp.

During operation, the integrating sphere emits diffuse radiation, which is well–calibrated in

the wavelength range from 380 to 2500 nm. Thus, the integrating sphere provides sufficient

22 3. Experimental

Figure 3.4: Scheme of the setup for the absolute radiometric calibration of the AisaEAGLE imagingspectrometer using an integrating sphere.

coverage of the AisaEAGLE effective wavelength range. The calibration factors in units of

Wm−2 nm−1 sr−1ADU−1 for each spatial pixel are obtained from:

fc(λ, npix) =Scal(λ)

Smeas(λ, npix), (3.6)

where Scal defines the calibrated output of the integrating sphere in Wm−2 nm−1 sr−1 and

Smeas defines the detected signal of each spatial and spectral pixel in ADU. Figure 3.5 illus-

trates the spectral calibration factors fc derived from the absolute calibration of AisaEAGLE

as a function of the spatial pixel number. The corresponding calibration uncertainty is ex-

emplarily illustrated for the first and central spatial pixel in Fig. 3.6a and for three selected

wavelengths in Fig. 3.6b. Those wavelengths are selected to cover both ends of the detectable

wavelength range as well as the largest and lowest uncertainty ranges.

Figure 3.5: Calibration factors from the absolute radiometric calibration of AisaEAGLE.


Figure 3.6: Calibration factors from the absolute radiometric calibration of AisaEAGLE. Averageand calibration uncertainty (a) of first and central spatial pixel as a function of wavelength and (b)at 400 nm, 530 nm, and 970 nm wavelength as a function of the spatial pixel number.

The spectral calibration factors are largest at both ends of the detectable wavelength range

and show a minimum at wavelengths between 500 and 600 nm. Largest values are found

for the longest wavelengths. On the spatial axis, the calibration factors show a distinct

minimum for the center pixels and two symmetrical maxima compared to the central pixel

close to the edge of the sensor line. The significance of these maxima increases with increasing

wavelength.

3.2.2 Dark Current

Another parameter that has to be considered during the calibration procedure and during the

operational application is the dark current. It is a signal generated by the instrument itself,

which has to be characterized and subtracted from the measurements. It originates from

the thermal movement of the CCDs molecules, which leads to the formation of free charge

carriers increasing the signal also in the unlighted state. The dark current is determined

using a shutter inside the optical path of AisaEAGLE. In the operational mode, a dark

measurement with a temporal duration of 3 s is performed subsequently of each scan. During

the radiometric calibration, two separate measurements are performed. A measurement with

opened shutter, illuminated detector (Slum) and another one with closed shutter (Sdark). For

both measurements, the same integration time is applied. Figure 3.7 illustrates the dark

current of AisaEAGLE as a function of spectral bands and spatial pixel number. The dark

measurements are averaged separately for each spatial pixel. The resulting value represents

the dark current. It is subtracted from the dedicated illuminated measurements, before the

calibration factors are calculated. This procedure makes the calibration factors independent

of the dark current. Figure 3.7 reveals that the dark current from AisaEAGLE measurements

yields no significant wavelength dependence over the detectable wavelength range. The

measured dark current is almost constant at 50ADU± 3ADU (1.2% of detection limit).

24 3. Experimental

Figure 3.7: Dark current of AisaEAGLE. Average (colored solid lines) and uncertainty (gray-shadedarea) (a) of first and central spatial pixel as a function of wavelength and (b) at 400 nm, 530 nm,and 970 nm wavelength as a function of the spatial pixel number.

Furthermore, a dependence on temperature and integration time was not established. The

temperature dependence was tested with a comparison of dark current measurements at 5

and 20. Therefore, this value is more a constant offset than a typical dark current, generated

by the instruments temperature.

3.2.3 Linearity

Tests have proven a linear relation between the detected signal and the intensity of the

radiation source, see Fig. 3.8a. It shows the saturation of the center spatial pixel for different

wavelength as a function of the output of the integrating sphere. This saturation increases

linearly with increasing intensity of the lamp; the linear fit matches the single measurement

points. As a function of the integration time, Fig. 3.8b illustrates the pixel saturation (in

%), which is the measured raw signal after dark current subtraction (%), normalized to the

maximum saturation of the CCD and current output of the lamp. This pixel saturation

increases linearly with increasing integration time. The linear fits match the single data

points (R2=0.99).

This linear relation allows a normalization of the calibration factors by the integration time.

This simplifies the data evaluation to the subtraction of the particular measured dark current

and multiplication of the measured signal by the normalized calibration factors. Therefore,

the relation between the measured raw data and the calibrated radiances Iλ for each spatial

and spectral pixel are given by:

Iλ(npix) = fc(λ, npix) ·Slum(λ, npix)− Sdark(λ, npix)

tint. (3.7)


Figure 3.8: Measured raw signal after dark current subtraction (%), normalized to the maximumsaturation of the CCD and current output of the lamp, as a function of the (a) intensity of theintegrating sphere and (b) applied integration time. The data are exemplarily depicted for the centerspatial pixel (npix =512) and the six selected wavelengths of λ=400; 500; 600; 700; 800; 900 nm.

3.2.4 Spectral Calibration

The manufacturer provides a spectral calibration, mapping wavelengths to the spectral pixel

number. A test was carried out in the laboratory using spectral lamps with defined emission

lines. The applied Penray spectral lamps and spectral emission lines are listed in Tab. 3.2.

The lamps are quite thin; it is difficult to fully cover the whole detector of the AisaEAGLE.

Therefore, during the test of the wavelength calibration of AisaEAGLE, the spectral lamps

were placed within an integration sphere to better illuminate the detector. A comparison

of those pixels showing the largest amplitude with the wavelength calibration file that was

provided by the manufacturer revealed sufficient agreement on all checked emission lines.

Table 3.2: Emission lines of spectral lamps applied for the wavelength calibration.

Lamp Wavelength of Emission Lines (nm)

Argon 727.29 763.51 826.45 866.79 922.45 965.78Mercury 404.66 435.83Neon 621.73 692.95

3.2.5 Measurement Uncertainties

The measurement uncertainty of AisaEAGLE results from uncertainties in the absolute cali-

bration and (less importantly) the measured signal. The uncertainty in the absolute calibra-

tion results from the uncertainty of the integrating sphere. The manufacturer specifies this

uncertainty to be about ± 6% for the wavelength range detected by the AisaEAGLE.

26 3. Experimental

The uncertainty of the measured signal is related to its signal–to–noise (SNR) ratio. The

manufacturer specifies the SNR of the AisaEAGLE to be in a range of 350:1 to 1400:1,

depending on the band configuration (spatial and spectral binning). With a dynamic range

of the single pixels from 0 to 4096ADU, the uncertainty in the measured signal, which

is generated by the SNR can be neglected compared to the uncertainty generated by the

integration sphere. Depending on the band configuration, it exhibits maximum values of

only 0.07 to 0.29% (inversely proportional).

3.2.6 Smear correction

Since the AisaEAGLE detector is based on CCD technique, it is necessary to correct for the

smear effect in calibration and measurement data. The smear effect occurs during the read-

out process of the collected photoelectrons, which are shifted step by step from one spectral

pixel to the neighbouring one into the direction of the read-out unit (Fig. 3.9). The read-out

process is not infinitely fast. Due to the fact that radiation can still reach the sensor during

read-out, the pixels are contaminated by an additional signal. The read-out process begins

at the red end of the spectral range. Therefore, the additional signal (smear effect) is larger

for shorter wavelengths, because the corresponding charges have to traverse the entire chip.

Figure 3.9: Illustration of the read-out process and the smear effect. The gray bar on the leftside illustrates the read-out unit. The arrows indicate the shifting direction of the photoelectrons.The magnitude of the signal of each pixel is indicated by the size of the circles. The smear effectis illustrated for one spatial pixel, which is exposed to additional illumination at one spectral pixel(yellow) during the read-out process.

The measurements are corrected for the smear effect by applying the correction algorithm:

x1 = y1,

x2 − Sc · y1 = y2,

x3 − Sc · (y1 + y2) = y3,

· · ·,xn − Sc · (Σn

i=1yi−1) = yn, (3.8)

where xi are the uncorrected and yi are the corrected digital counts with the wavelength

index i=1,. . . ,n. The smear correction factor Sc= tread-out / tint is the ratio of the duration


of a read-out step (tread-out=1.33 µs) to the total integration time. For the first read-out step

no correction is necessary, since the counts from the first pixel are shifted directly into the

read-out unit. During the whole read-out process, the illumination of all pixels is assumed

to remain constant. Therefore, new charges are still generated while the original charges are

already shifted towards the read-out unit. The original charge from a given pixel increases by

the radiation that falls on the pixel the charge travels through. The increase is proportional

to the smear correction factor Sc as well as the illumination of the pixels (see the fourth line

of Fig. 3.9).

The smear effect must be taken into account for each measurement as well as for the cal-

ibration. Tests have shown that during atmospheric measurements the signal outside the

effective wavelength range can be neglected for the smear correction (which significantly re-

duces the required data storage space). This is because solar spectral radiance is typically

larger for shorter (400 nm) than for longer (900 nm) wavelengths. This does not hold for the

calibration. The halogen calibration lamp of the integrating sphere is colder than the Sun

and emits radiation with a maximum in the near-infrared range (1000 nm) and low values

at shorter wavelengths (400 nm). Consequently, the wavelength pixels outside the effective

wavelength range above 1000 nm receive a significant amount of radiation.

Figure 3.10: (a) Spectral radiance measured with AisaEAGLE, for smear corrections consideringdifferent wavelength intervals in the calibration: 100–1300 nm (solid line), 400–1000 nm (dashed line).(b) Differences between the spectral radiances shown in panel (a).

A comparison between calibration radiance measurements derived with and without including

the wavelength pixels outside the effective wavelength range above 1000 nm is shown in

Fig. 3.10. Significant differences are observed for wavelengths below 500 nm, which agrees

with the theory of the smear effect. Differences range from 3% at 970 nm wavelength to

13% at 400 nm wavelength. Therefore, it is necessary to use the entire AisaEAGLE spectral

range during calibration, even though it is not used during data evaluation.

28 3. Experimental

3.3 Observation Geometries and Scattering Angle Derivation

Spectral radiance measurements with high spatial resolution obtained from the AisaEAGLE

imaging spectrometer are used in this thesis to identify the shape of ice particles in cirrus.

Since each spatial pixel refers to a specific viewing zenith angle θ, each spatial pixel receives

scattered radiation from a different solid angle Ω. This can be referred to features of the

scattering phase function. Figure 3.11 illustrates the measurement geometry needed to derive

the scattering angles ϑ for each spatial pixel.

Figure 3.11: Illustration of the ground-based and airborne AisaEAGLE measurement geometry ina Cartesian coordinate system (x, y, z) with position of the Sun (S), a scattering cloud particle (C)and the AisaEAGLE detector (D). θ0 is the solar zenith angle, φ0 the solar azimuth angle, ϑ thescattering angle, and βi the viewing angle of the corresponding pixel i.

According to Eq. (2.16), for airborne (AB) and ground–based (GB) applications, the scatter-

ing angle ϑ is calculated from the scalar product of the vector of the incoming solar radiation

(−→SC) and the vector of the radiation scattered into the sensor direction (

−−→CD):

ϑ = arccos

( −→SC · −−→CD

|−→SC| · |

−−→CD|

). (3.9)

The applied coordinate system is related to the coordinate system of the sensor (mathematical

positive). Thus, the orientation of the scattering plane is given by the orientation of the

3.3. Observation Geometries and Scattering Angle Derivation 29

AisaEAGLE sensor line. Related to ground–based observations this results in measurements

of the transmitted radiance I↓λ and related to airborne observations in measurements of the

reflected radiance I↑λ. In contrast to Eq. (2.16), no azimuthal averaging is performed and the

solar azimuth angle has to be considered as well. Regarding the Cartesian coordinate system

of the sensor (Fig. 3.11),−→SC and

−−→CD yield the following:

−→SCGB =

δ · sin∆φ

−δ · cos∆φ

−δ/tanθ0

−−→CDGB =

0

−h · tanβi−h

−→SCAB =

−δ · sin∆φ

−δ · cos∆φ

δ/tanθ0

−−→CDAB =

0

−h · tanβi−h

(3.10)

Here, δ is the vector between S and C projected onto the x-y-plane. The values of βi are

considered positive for pixels viewing into the direction of the Sun (solid arrows in Fig. 3.11)

and negative for pixels viewing away from the Sun (dotted arrows in Fig. 3.11). ∆φ is the

relative difference between the solar (φ) and the sensor (φSen) azimuth angles. φSen is given

by the viewing azimuth angle of the spatial pixel number 1024.

Solving the scalar product of Eq. (3.9), using the definitions for the vectors−→SCGB and

−−→CDGB

from Eq. (3.10), the scattering angle ϑ is obtained by:

ϑGB = arccos

(δh · cos∆φ · tanβi + δh/tanθ0√

h2tan2βi + h2 ·√

δ2sin2∆φ+ δ2cos2∆φ+ δ2/tan2θ0

)

= arccos

(cos∆φ · tanβi + 1/tanθ0√1 + tan2βi ·

√1 + 1/tan2θ0

). (3.11)

Multiplying tanθ0/tanθ0 to Eq. (3.11) and using the following relations:

1 = sin2x+ cos2x (3.12)

sinx =√

1− cos2x =tanx√

1 + tan2x(3.13)

cosx =√1− sin2x =

1√1 + tan2x

, (3.14)

Eq. (3.11) simplifies to:

ϑGB = arccos (cos φ0 · sin θ0 · sin βi + cos θ0 · cos βi) . (3.15)

Consequently, regarding airborne applications, the scalar product of Eq. (3.9) yields:

ϑAB = arccos (cos φ0 · sin θ0 · sin βi − cos θ0 · cos βi) . (3.16)

30 3. Experimental

The final Eq. (3.15) and (3.16) differ from Eq. (2.16) by the additional azimuthal dependence,

which is given by the term cosφ0. Both Eqs. (3.15) and (3.16) imply that the largest coverage

of the scattering angle range can be derived for an orientation of the AisaEAGLE sensor

line along the direction of the solar azimuth (∆φ = 0). For a perpendicular orientation

(∆φ = 90) of the sensor line with regard to the solar azimuth angle φ, the first term of

Eq. (3.15) and Eq. (3.16) yields ϑ = 0. In this case, only a narrow range of scattering angles

close to the particular solar zenith angle can be derived. Conversely, for an orientation of

the AisaEAGLE sensor line along the solar azimuth angle φ (∆φ = 0), the absolute range

of the detectable scattering angles is equal to the FOV of the AisaEAGLE and the part of

the scattering phase function that is covered by the measurements is defined by the solar

zenith angle θ0 (see Fig. 3.12b). For both extreme cases (∆φ = 0, ∆φ = 90), Fig. 3.12

illustrates and Tab. 3.3 quantifies the detectable scattering angle range as a function of the

solar zenith angle θ0. The given values are representative for measurements with a 36.7 lens,

as it was used for the ground-based measurements from the CARRIBA campaign, presented

in Sect. 4.1. Here, in terms of comparability, the 36.7 lens is also applied for the listed

airborne calculations, although during VERDI a 36.3 lens was applied.

Figure 3.12: Scattering angle range that can be detected from ground-based and airborneAisaEAGLE measurements of the solar spectral radiance I↓λ and I↑λ. The values are representa-tive for a 36.7 lens and exemplarily depicted for the first, the central and the last spatial pixel, whilethe orientation of the AisaEAGLE sensor line is set (a) perpendicular (∆φ = 90) and (b) parallel(∆φ = 0) to the direction of the solar azimuth angle φ.

The values listed in Tab. 3.3 reveal that for the special case of θ0 = 0, the detectable

scattering angle range is equal for measurements perpendicular or parallel to the direction

of the solar azimuth angle φ. However, for this special case the instruments inlet would

have to be pointed exactly into the direction of the Sun (ground–based application). Those

measurements would then very likely be overexposed unless the cloud optical thickness is

not exceeding a value of τ =10. Due to the strong forward scattering peak of ice crystals,

this threshold could be even to small for cirrus. However, a cirrus with an optical thickness

in that range is rather rare. Therefore, the pointing direction of the instruments inlet needs

3.3. Observation Geometries and Scattering Angle Derivation 31

to be different from the Sun’s position. Doing so, the detectable scattering angle range is

rapidly decreasing for a perpendicular orientation of the sensor line (∆φ=90); a parallel

orientation is advisable (∆φ=0).

Table 3.3: Scattering angle range that can be detected from AisaEAGLE measurements of solarspectral radiance I↓λ and I↑λ. The values are representative for a 36.7 lens and exemplarily depictedfor the first, the central and the last spatial pixel. The orientation of the sensor line is set perpendicular(∆φ = 90) or parallel (∆φ = 0) to the direction of the solar azimuth angle φ.

∆φ() θ0() ϑPixel 1(

) ϑPixel 512() ϑPixel 1024(

) Total ϑ Range ()

GB | AB GB | AB GB | AB GB | AB0 0 18.35 | 161.65 0 | 180 (-)18.35 | 161.65 36.7 | 18.350 15 33.35 | 146.65 15 | 165 (-)3.35 | 176.65 36.7 | 30.00 30 48.35 | 131.65 30 | 150 11.65 | 168.65 36.7 | 36.70 45 63.35 | 116.65 45 | 135 26.65 | 153.35 36.7 | 36.70 60 78.35 | 101.65 60 | 120 41.65 | 138.35 36.7 | 36.70 75 93.35 | 86.65 75 | 105 56.65 | 123.35 36.7 | 36.70 90 108.35 | 71.65 90 | 90 71.65 | 108.35 36.7 | 36.7

90 0 18.35 | 161.65 0 | 180 18.35 | 161.65 36.7 | 36.790 15 23.53 | 156.46 15 | 165 23.53 | 156.46 17.1 | 17.190 30 34.71 | 145.28 30 | 150 34.71 | 145.28 9.42 | 9.4290 45 47.84 | 132.16 45 | 135 47.84 | 132.16 5.68 | 5.6890 60 61.67 | 118.33 60 | 120 61.67 | 118.33 3.34 | 3.3490 75 75.78 | 104.22 75 | 105 75.78 | 104.22 1.56 | 1.5690 90 90.00 | 90.00 90 | 90 90.00 | 90.00 0.00 | 0.00

33

4 Subtropical Cirrus - Ground-Based

Observations

To analyze cirrus inhomogeneities, fields of cirrus optical thickness τci are used. In the fol-

lowing the approach to derive these fields of τci from ground-based measurements of down-

ward spectral radiance (I↓λ) fields is introduced. Those fields of I↓λ were collected with the

AisaEAGLE imaging spectrometer during the CARRIBA campaign, which is introduced in

Sect. 4.1. Based on this measurements, a new method is presented to retrieve τci. Section 4.4

shows that by comparing measured and simulated I↓λ as a function of scattering angle ϑ, some

evidence of the prevailing cirrus crystal shape is obtained. Subsequently, this shape is used

to substantiate the retrieval of τci, for which a first analysis regarding cloud inhomogeneities

is applied in Sect. 4.5. The sensitivity of the retrieval method with respect to surface albedo,

effective radius (reff), cloud altitude and ice crystal shape is quantified in Sect. 4.6. Parts of

this chapter have been published in Schafer et al. (2013).

4.1 CARRIBA (Clouds, Aerosol, Radiation, and tuRbulence in the

trade wInd regime over BArbados)

In April 2011, the second campaign of the CARRIBA project was performed in Barba-

dos. The measurements were characterized by consistent meteorological conditions in the

trade wind regime with regular occurrence of high ice clouds (Malkus, 1954, 1956, 1958;

Siebert et al., 2013; Werner et al., 2013). The aim of CARRIBA was to investigate micro-

physical and radiative processes within and next to shallow trade wind cumuli by helicopter-

borne and ground-based observations (e.g. Siebert et al., 2013; Werner et al., 2013, 2014).

However, also cirrus has frequently been observed by the ground-based instrumentation.

During CARRIBA, the imaging spectrometer AisaEAGLE was located in the Barbados

Cloud Observatory (BCO; Stevens et al., 2015) of the Max Planck Institute for Meteorology

(Hamburg, Germany) at Deebles Point (13.15N, 59.42W), a cape at the East coast of

Barbados. Figure 4.1 shows a map with the location of the BCO and the setup of the

station.

Measurements with a Raman LiDAR and a cloud radar as well as radiosonde data are

available from the same site. Table 4.1 lists the instruments installed at the BCO and their

most relevant specifications. In parallel to the AisaEAGLE radiance measurements, all-sky

images were collected every 15 s to monitor the cloud situation (cloud coverage, cloud type,

heading). Downward spectral radiance was measured under inhomogeneous cloud cover on 14

different days. Each day, two hours of data were collected in parallel to the helicopter flights.

34 4. Subtropical Cirrus - Ground-Based Observations

Figure 4.1: Site of the AisaEAGLE radiance measurements during the CARRIBA campaign atDeebles Point on the east coast of Barbados.

Table 4.1: Instrumentation at the BCO during CARRIBA. Only those instruments and measuredquantities are listed, which contributed to the data analysis within the scope of this thesis.

Instrument Measured Quantity Unit Range

AisaEAGLE Radiance Wm−2 nm−1 sr−1 λ=400–970 nm

CANON Camera RGB Radiance Wm−2 nm−1 sr−1 λ=(446,530,591) nm

Raman LiDAR Cloud Altitude m z=0–15 kmCloud Phase Cloud Free, Liquid, Ice

Ceilometer Cloud Base Altitude m z=0–15 km, ∆z=15m

Radiosonde Air Pressure hPaTemperature CRelative Humidity %Wind Field m s−1,

While trade wind cumuli were not always present, cirrus clouds were observed during each

measurement. In the following, four measurement cases are evaluated with only cirrus clouds

to exclude any radiative effects by low cumuli. During CARRIBA, a lens with an opening

angle of AisaEAGLE of about 36.7 was mounted. With regard to the slow movement of the

cirrus, a sufficient frame rate of 4Hz was used. The integration time was chosen between 10

and 30ms, depending on the illumination of the cloud scene.

4.2 Method to Retrieve Cirrus Optical Thickness

For the retrieval of τci from the measured downward spectral radiance I↓λ transmitted

through the cirrus, radiative transfer calculations are performed. The radiative transfer

solver DISORT 2 (DIScrete Ordinate Radiative Transfer) is applied. Input parameters

such as cloud optical properties, aerosol content and spectral surface albedo are provided

by the library for Radiative transfer calculations (libRadtran, Mayer and Kylling, 2005).

The HEY parameterization (Hong Emde Yang; Yang and Liou, 2000) is used to describe

4.2. Method to Retrieve Cirrus Optical Thickness 35

the scattering properties of ice crystals. It uses pre-calculated ice cloud optical properties

including full phase matrices generated with the models by Yang and Liou (2000).

The simulations are performed at 530 nm wavelength. This wavelength is chosen to match the

wavelength of the LiDAR measurements at BCO. Since BCO is located at the far end of this

cape, the measurement site is surrounded by water, rocks and grass. For simplification the

surface albedo in the radiative transfer simulations is assumed to be only water, as derived by

Wendisch et al. (2004), providing a value of 0.068. libRadtran supplies calculated Mie tables

for rural, maritime, urban and tropospheric aerosol size distributions given in Shettle (1989).

Because the measurements were performed in the vicinity of the coast, the maritime type is

chosen as aerosol input for libRadtran. The cloud altitude and vertical extent is determined

from the LiDAR measurements performed at BCO, see Fig. 4.2.

Figure 4.2: Cloud masks derived from LiDAR measurements at the BCO with 10min temporalresolution for (a) 9 April 2011, (b) 16 April 2011, (c) 18 April 2011, and (d) 23 April 2011. Blackcolored areas mark data gaps. Separation in liquid water clouds (blue), ice clouds (red), and cloudfree areas (white) with a vertical accuracy of 60–660m depending on the altitude.

For the simulations, a fixed reff has to be defined as no direct retrieval from AisaEAGLE is

possible. For this, a value of 20 µm is assumed. The assumed reff is taken from MODIS data

(Collection 5) as estimate for the clouds in the area close to BCO. libRadtran adapts the

IWC with respect to the prescribed reff and simulated τci (Mayer, 2005). Therefore, a direct

retrieval of the IWC is not possible, because the method is not sensitive to reff. Furthermore,

the imaging measurements require an accurate description of the sensor geometry in the

simulations as shown in Fig. 3.11. The sensor was aligned horizontally. The sensor azimuth

angle was not measured directly but estimated from measurements during the time when the

Sun’s azimuthal position was in the direction of the sensor line. If both azimuth angles are

equal, the measurements will be overexposed with a distinct maximum. The sensor azimuth

angle is derived from the time of that maximum. The viewing zenith angle is given by the

sensor FOV, which is β=± 18. Related to this range, the downward solar radiance I↓λ,cal is

calculated for angles with 0.3 steps.


Using these input parameters, downward solar radiance I↓λ,cal is simulated as a function of

τci. The simulations are performed for the FOV of AisaEAGLE over the period of each

measurement. Thus, a simulated grid (look–up table, LUT) of possible radiances and cor-

responding τci is available for each time stamp of the measurement and each spatial pixel.

The retrieved τci is derived by linear interpolation of the simulated radiances from the LUT

to the measured value for each spatial pixel.

Figure 4.3: Simulated radiance at 530 nm as a function of τci for different solar zenith angles.

Figure 4.3 exemplifies radiance simulations for the solar zenith angles of 30, 45, and 60,

a solar azimuth angle of 90, and a cirrus with ice crystals in the shape of solid columns.

The base of the cirrus is at 11 km altitude. Figure 4.3 indicates that the retrieval of τci is

ambiguous. For example, at θ0=30 a radiance of 0.2Wm−2 nm−1 sr−1 corresponds to τciof either 1 or 15. Recently, Bruckner et al. (2014) introduced a multispectral cloud retrieval

method that avoids this ambiguity. Based on a method by McBride et al. (2011), it uses

three ratios of transmitted radiance at visible and near-infrared wavelengths to create 3D

LUT without ambiguity. However, currently the AisaEAGLE radiance measurements are

restricted to the visible wavelength range. Thus, this method cannot be adopted yet. The

ambiguity has to be considered using additional information of the estimated τci. In the case

of thin cirrus (τci less than about 3–4), the retrieval results for low values of τci must be

used, for optically thicker cirrus the section for large τci must be applied. Thus, independent

knowledge of the expected range of τci is important to avoid the ambiguity in the retrieval.

During CARRIBA, this supplementary information was provided by all-sky images and Li-

DAR measurements. The all-sky images do not give a quantitative value of τci, but they are

evaluated qualitatively. An experienced observer is able to judge whether a given cloud has

an optical thickness higher or lower than the maximum indicated in Fig. 4.3. All retrieved

τci presented within this study are in the range left of the maximum.

4.3 Measurement Cases

Four data sets from the CARRIBA project from different days are evaluated: 9, 16, 18 and

23 April 2011. These days showed persistent cirrus with no other clouds below. An overview

of the main characteristics of the evaluated measurement periods is summarized in Tab. 4.2.

4.3. Measurement Cases 37

Table 4.2: Characteristics of the evaluated measurement periods.

Date 9 April 16 April 18 April 23 April

Label C-01 C-02 C-03 C-04Swath (km) 7.3 8.0 8.6 7.3Length (km) 15.6 40.5 44.1 13.3Start Time (UTC) 13:26 13:43 13:43 16:45θ0 () 36.7 28.6 28.5 14.5Cirrus Heading SW → NW NW → SW WSW → ESE SSW → NNEAppearance inhomog. homog. homog. inhomog.Cloud Altitude (km) 11–15 12–15 13–15 11–14I↓ ± σI (Wm−2 nm−1 sr−1) 0.08± 0.02 0.11± 0.02 0.10± 0.03 0.16± 0.03τci ± στ 0.41± 0.17 0.28± 0.09 0.20± 0.03 0.05± 0.04Covered ϑ Range () 35.1–47.1 32.6–37.9 21.2–48.2 12.2–36.3

Figure 4.4a–d show all-sky camera images from the beginning of the four cases. Within each

image, the red arrow indicates the movement of the cirrus during the analyzed period. The

heading is derived by comparing the position of clouds in the sequence of all-sky images

(15 s time resolution). The blue box indicates the area covered by the AisaEAGLE radiance

measurements, i.e. the area of cirrus, which is heading across the sensor line during the

measurement period. Due to the fact that the AisaEAGLE was not orientated perfectly in

perpendicular direction to the cirrus heading, the covered area is not a rectangle in most

cases.

Figure 4.4: All-sky images from the beginning of the evaluated AisaEAGLE radiance measurementsfor (a) 9 April, (b) 16 April, (c) 18 April and (d) 23 April 2011 with the flow direction of the cirrus(red arrow) and FOV of the AisaEAGLE radiance measurements (blue). Orientation given by blacklines and capital letters.

During all four measurement cases, τci is estimated to be less than 3–4. That means that the

ambiguity of Fig. 4.3 is avoided in all four cases. The cirrus field on 16 and 18 April was more

homogeneous than that observed on 9 and 23 April. On 23 April, a 22 halo was identified

on the all-sky images but unfortunately was not covered by the FOV of AisaEAGLE.

Fields of transmitted downward radiance I↓λ as measured by AisaEAGLE for the four cases

are presented in Fig. 4.5. The radiance is given for 530 nm in 2D color-scale images for all

1024 spatial pixels on the abscissa and the time of measurement on the ordinate.


Figure 4.5: Two-dimensional images of the evaluated AisaEAGLE radiance measurements at 530 nmwith the measured I↓λ (Wm−2 nm−1 sr−1) given in color scales.

The cloud structure seen in the all-sky camera images in Fig. 4.4a–d is imprinted in the

radiance field. The average values I↓λ of the measured radiance are given in Tab. 4.2. The

highest value of I↓ was observed on 23 April 2011 and the lowest on 9 April 2011.

Especially for 18 April 2011 it is evident that the image gets brighter from the left to the

right side. During this day the sensor line of AisaEAGLE was orientated from North-West

(pixel 1) to South-East (pixel 1024) while the Sun was in the East at the same time. This

brightening is caused by enhanced scattering for small scattering angles, corresponding to the

shape of the scattering phase function of ice crystals (see Fig. 4.6). Therefore, the radiative

transfer calculations to retrieve τci need to take into account the exact alignment of the sensor

line and the exact position of the Sun. If the sensor orientation is carefully considered, the

retrieval will account for this brightness effect caused by enhanced forward scattering by ice

crystals.

Using the calculated scattering angles derived for each spatial pixel from Eq. (3.15), the

I↓λ illustrated in Fig. 4.5 are now displayed as a function of scattering angle as shown in

Fig. 4.7. The scattering angles are symmetrical for each pixel to the pixel closest to the

Sun. If the Sun’s azimuthal position is almost perpendicular to the sensor line, a minimum

appears in the detected scattering angles per spatial pixel. In such cases, the plot of I↓λ as

a function of the scattering angle would have overlapping sections. For clarity, one of those

sections is assigned a negative sign in Fig. 4.5. Note that the images are not rectangular

due to the movement of the Sun during the measurement period. The advantage of the

4.4. Retrieval of Ice Crystal Shape 39

Figure 4.6: Scattering phase functions for (a) the different ice crystal shapes at 20 µm and (b) solidcolumns, calculated for the three effective radii for the retrieval in this study. The gray bar indicatesthe captured scattering angle range during the measurements.

illustration using scattering angles is that structures in the image related to the scattering

phase function of the ice crystals occur in a fixed position throughout the time series, as can

be seen for 18 April 2011. The radiance always increases with decreasing scattering angle,

which is a typical characteristic of the forward scattering by cloud particles.

4.4 Retrieval of Ice Crystal Shape

The ice crystal shape is estimated from the directional distribution of radiance, considering

the scattering phase function of different ice crystals. While on 9, 16 and 18 April no halo was

visible, the 22 halo was observed on 23 April (compare Fig. 4.4). Thus, regular ice crystals

like columns or plates must have been present on that day. For the first three cases, irregular

ice crystals are more likely, because the crystals did not produce a halo. The directional

scattering features are analyzed in detail with the AisaEAGLE measurements.

Figure 4.8 shows the average measured downward solar radiance I↓λ and its standard deviation

as a function of the scattering angle ϑ for 18 April 2011. The standard deviation depends

on the scattering angle and is calculated in intervals of ∆ϑ=0.3. Additionally, Fig. 4.8

includes simulations of downward solar radiance for different values of τci and different ice

crystal shapes. Figure 4.8a shows that for simulations assuming rough aggregates, no halo

appears in the calculated radiance. However, for calculations with solid columns, plates as

well as a mixture of ice crystals, the two halo regions are well defined in the simulation results.

Furthermore, the best agreement between simulated and measured downward radiance I↓λ is

found for rough aggregates. For this reason, the τci for 18 April 2011 is retrieved by assuming

rough aggregates for the ice crystal shape in Sect. 4.5.

A similar analysis for 23 April 2011 is presented in Fig. 4.9. Enhanced radiance is measured

at scattering angles between 22 and 26, which indicates the presence of a 22 halo. The

halo is quite hard to identify in Fig. 4.7 due to the cirrus inhomogeneities and probably

a mixture of shapes. Therefore, the halo is quite weak. The averaged radiance displayed


Figure 4.7: Time series of the measured downward solar radiance I↓λ during the four measurementcases as a function of scattering angle for each spatial pixel. The range of the abscissa of each imageis fitted to the corresponding range of covered scattering angles.

in Fig. 4.9 confirms this. The halo can be seen in the averaged data. However, due to the

low τci of 0.2, the maximum of the enhanced radiance within the halo region is relatively

low. Concerning the ice crystal shape, best agreement is found for a mixture of different ice

crystal shapes, while for aggregates the mismatch of the halo is obvious. A retrieval of the ice

crystal shape is difficult because the cirrus was very inhomogeneous, as indicated by the high

standard deviation. The variability of the radiances is about ± 0.03Wm−2 nm−1 sr−1, which

corresponds to a deviation of 20% to the mean value. Therefore, the radiance fluctuations

cannot be related to the scattering phase function. Considering that the analyzed sequence

on 23 April is short, with only about 6 minutes duration, it is more likely that changes of τciaccount for the structure in the radiance. Therefore, in the following retrieval of the τci for

23 April 2011, ice crystals in the shape of solid columns (default setting in libRadtran) are

assumed.

For 9 and 16 April 2011 the retrieval of the ice crystal shape within the cirrus is not possible.

Due to the geometry (wind direction, sensor alignment, solar position), only a narrow range

(32–47, 25–37) of scattering angles outside the 22 halo range is observed and the clouds are

too inhomogeneous. The detected scattering angles just cover the edge of the halo regions.

Therefore, the radiative transfer calculations to retrieve the τci in Sect. 4.5 are performed for

solid columns. An estimate of uncertainties related to the shape assumption is provided in

Sect. 4.6.

4.5. Retrieval Results for Cirrus Optical Thickness 41

Figure 4.8: Measured and simulated I↓λ as a function of scattering angles. The standard deviationof the measurement is represented by the gray shade. Measurements are from 18 April 2011. Thesimulations were performed for different τci and an assumed ice crystal shape of (a) rough aggregates,(b) solid columns, (c) plates, and (d) mixture.

4.5 Retrieval Results for Cirrus Optical Thickness

The τci retrieved by the presented method are displayed in Fig. 4.10. The measurement time

and the pixel number are converted into distances along and across the swath. For this, the

altitude of the cloud base is used to derive the values for the abscissa. The average wind

velocity in that altitude, derived from the HYbrid Single-Particle Lagrangian Integrated

Trajectory (HYSPLIT) model provided by the Air Resources Laboratory (ARL) of NOAA,

is used to convert the ordinate into a unit of distance. For 18 April 2011 the retrieved τciindicates that the cloud is quite homogeneous. This confirms that the observed increase in

radiance (Figs. 4.5 and 4.7) results from enhanced forward scattering of ice crystals and has

been considered correctly by the model. For the other measurement cases, inhomogeneous

cirrus is observed with large areas of cloudless regions in between.

Figure 4.11 shows frequency distributions of the retrieved τci. They are normalized by

the total of the retrieved τci with a bin size of 0.01 in τci. The largest τci are found for

9 April 2011 (peak at τci=0.35), the smallest for 23 April 2011 (peak at τci=0.05). The

frequency distributions for 16 and 18 April 2011 show peaks at τci close to each other (peaks


Figure 4.9: Measured and simulated I↓λ as a function of scattering angles. The standard deviationof the measurement is represented by the gray shade. Measurements are from 23 April 2011. Thesimulations were performed for different τci and an assumed ice crystal shape of (a) rough aggregates,(b) solid columns, (c) plates, and (d) mixture.

at τci=0.20/ 0.25). Main differences are related to the number and width of the modes. The

frequency distribution for 9 April 2011 is comparatively broad (τci=0.0–1.0) and clearly has

a bimodal shape (second smaller peak at τci=0.2). The frequency distribution from 16 April

2011 is broad as well (τci=0.1–0.7) with a tendential bimodal shape (second undefined peak

at τci=0.15). In contrast, the frequency distributions for 18 April 2011 and 23 April 2011

are narrow (τci=0.15–0.3/ 0.0–0.25) and monomodal. Broader frequency distributions and

bimodal shapes are an indication for inhomogeneous cloud structures.

The average and standard deviation of the retrieved τci are a further indication for the

inhomogeneity of a cloud situation. High standard deviations compared to the average values

indicate a larger heterogeneity of the detected cloud situation. The particular values for each

measurement case are listed in Tab. 4.2. Although the frequency distribution for 23 April

2011 shows a narrow peak compared to the other cases, the standard deviation reveals that

this case was rather inhomogeneous, generated by the mix of cloudless and cloudy parts.

Thus, in comparison, the cirrus on 16 and 18 April 2011 were more homogeneous than those

on 9 and 23 April 2011. A more detailed analysis of the cirrus inhomogeneities including

a statistical evaluation based on inhomogeneity parameters and an evaluation regarding their

horizontal distribution is presented in Chapter 6.

4.6. Sensitivity Study 43

Figure 4.10: Time series of the retrieved τci during the four measurement cases for each spatialpixel. Abscissa and ordinate values are different due to different measurement conditions.

4.6 Sensitivity Study

A sensitivity study is performed to quantify the retrieval uncertainties with regard to the as-

sumptions made on the model input parameters. Uncertainties regarding the surface albedo,

effective radius, cloud base altitude, and ice crystal shape are tested. Only one of those

parameters is varied at one time and all other input parameters of the benchmark retrieval

are kept constant. The benchmark case uses a surface albedo of water (0.068 at 530 nm

wavelength), but AisaEAGLE was also surrounded by grass and sand and not just water.

To quantify the resulting uncertainties, the retrieval is repeated for a surface albedo of grass

and sand (0.073 and 0.314 at 530 nm wavelength; Feister and Grewe, 1995). The effective

radius reff is assumed to be 20 µm in the benchmark retrieval. The sensitivity study is per-

formed for 15 and 40 µm. This range is estimated from MODIS measurements for the time

of the four measurement cases. The τci was too low to be detectable by MODIS during the

period of the presented measurements. Therefore, the surrounding regions of Barbados are

used to derive the range of the effective radii. Another source of uncertainties is the cloud

base altitude. For the sensitivity study the cloud is lifted 4 km upward and 4 km downward.

For ground–based measurements and with no in situ observations available it is impossible

to determine the preferred cirrus crystal shape. While solid columns are assumed in the

benchmark retrieval, the sensitivity study is performed with plates and rough aggregates.


Figure 4.11: Normalized frequency distributions of τci for each of the four measurement cases. Thebin size is 0.01 units of τci.

The sensitivity is expressed as the relative difference between the results, calculated using

the average values of τci (indicated by τci):

∆τci = 100% ·(τci,BM − τci

τci,BM

)(4.1)

Table 4.3 gives the different averages over the entire scene, Fig. 4.12 shows the uncertainties

based on simulations. Radiances are simulated for τci ranging from 0 to 0.5. The simulated

radiances are then applied to the retrieval method where the benchmark properties are

assumed. The differences between the benchmark retrieval and the sensitivity study vary in

a range from less than one percent up to almost 90% as a function of the input parameters.

Table 4.3: Relative (%) and absolute difference of retrieved τci in comparison to benchmark case.

9 April 16 April 18 April 23 Aprilrel. abs. rel. abs. rel. abs. rel. abs.

αsurf=0.073 (Grass) 2.6 0.01 0.4 0.00 0.6 0.00 0.25 0.00αsurf=0.314 (Sand) 27.8 0.11 20.6 0.06 28.9 0.06 11.51 0.01reff=15 µm 0.5 0.00 1.1 0.00 0.5 0.00 -0.54 -0.00reff=40 µm -4.9 -0.02 -3.9 -0.01 -0.9 -0.00 -0.06 -0.00hcloud (4 km Lower) -0.45 -0.00 -0.28 -0.00 -0.14 -0.00 -0.06 -0.00hcloud (4 km Higher) 0.31 0.00 0.19 0.00 -0.05 0.00 0.05 0.00Shape (Plates) 14.80 0.06 75.3 0.21 85.6 0.17 12.26 0.01Shape (R. Aggr.) 23.3 0.09 26.1 0.07 33.1 0.07 17.11 0.01

Table 4.3 shows that for a surface albedo higher than the benchmark value, τci will be

overestimated. For a grass surface with a slightly larger albedo than water (0.073 compared

to 0.068), the overestimation is still small. However, for simulations with a sand surface

albedo (0.378), τci shows a significant overestimation. With a maximum of almost 29% on

4.6. Sensitivity Study 45

Figure 4.12: Retrieval results with regard to the sensitivity of (a) surface albedo, (b) effectiveradius, (c) cloud altitude, and (d) ice-crystal shape. Simulated for a solar zenith angle of θ0 =30,solar azimuth angle of φ=90, solid columns, 11–13 km cloud altitude, surface albedo of water andeffective radius of reff =20 µm. The benchmark case represents the one-to-one line.

18 April 2011 and a minimum of around 12% on 23 April 2011, the uncertainties are larger

than those resulting from the measurement uncertainty. This indicates that the surface

type has to be chosen correctly to enable accurate retrievals of τci. Fig. 4.12a confirms this

result. The retrieved τci for the synthetic radiance above water and grass are almost identical.

Compared to this, the retrieval result for a sand surface albedo shows larger values. The

overestimation of up to 30% seems to be relatively high; e.g. for very small τci the percental

difference can be quite large. However, the differences in the absolute values of τci are only

about ±0.1 and lower. Furthermore, this sensitivity study represents an extreme case, as

the grass at Deebles Point was patchy and rather dry, so the literature estimate for the sand

surface albedo is on the high side.

The downward solar radiance I↓λ depends approximately linearly on the ice crystals reff. Here,

a smaller reff yields an underestimation of the retrieved τci. For larger reff, the retrieved τciwill be overestimated. From the differences listed in Tab. 4.3, linearity can be assumed.

The absolute difference of reff=40 µm, referring to reff=20 µm, is four times higher than for

reff=15 µm referring to reff=20 µm. Approximately, this ratio is confirmed by the relative

differences in Tab. 4.3. However, the relative differences are in a range below 5% and the

absolute values show no significant change. Comparing the scattering phase functions in


Fig. 4.6b reveals that they are quite similar at most detected scattering angles with the

exception of the halo region and below 20 . Since the differences between the scattering

phase functions, calculated for different reff, appear mostly in the forward and backward

scattering range but not in the captured scattering angle range, this explains the small

variation found in the sensitivity study (Fig. 4.12b).

However, the contrast in the scattering intensity between 22 and the surrounding minima

for the three reff in Fig. 4.6b is large. Thus, in the special case of solid columns as well

as other hexagonal shapes, it is possible to estimate reff from the angular sampled spectral

radiance data. Unfortunately, those regions of the scattering phase function were covered

only twice during this study: on 18 April 2011 (with rough aggregates as the predominant

ice-crystal shape) and on 23 April 2011 (highly inhomogeneous cirrus). Here, the reff cannot

be retrieved: rough aggregates do not produce the 22 halo, and the cloud inhomogeneities

on 23 April caused radiance fluctuations that exceeded the intensity of the 22 halo.

Regarding a varied cloud base altitude, no significant changes in the retrieved τci are found.

The differences for all four cases are below 1%. Therefore, possible uncertainties of the

retrieved τci due to the cloud base altitude can be neglected. This is reproducible from the

retrieval results in Fig. 4.12c, which are congruent.

For the sensitivity test with regard to the cirrus crystal shape, Tab. 4.3 lists differences up

to almost 90%. The retrieved τci in Fig. 4.12d as well as the scattering phase functions in

Fig. 4.6a confirm this statement. Compared to the other parameters, the retrieval results

show larger differences to each other. This is related to differences in the scattering phase

functions for the scattering angle range captured during the four measurement cases. In

Fig. 4.12d the differences between the lines increase with increasing τci. Using plates or

rough aggregates instead of solid columns, τci will be underestimated in both cases. The

average of τci is larger by up to 0.2. Compared to the average values of the detected τcithis is not negligible. Therefore, the ice-crystal shape is important to accurately retrieve the

cirrus optical thickness from ground-based spectral radiance measurements.

Most of the scattering phase function features, which may help to identify the cirrus crystal

shape, are related to the two halo peaks at ϑ=22 and ϑ=46. To investigate the scattering

phase function in the range of the 22 halo, measurements at solar zenith angles θ0 between

15 and 30 are advisable. To detect the ϑ=46 halo, measurements at solar zenith angles

θ0 between 30 and 45 are most suitable (compare Tab. 3.3). To capture the largest possible

scattering angle range around those features, the sensor line has to be placed along the

direction of the solar azimuth angle φ0.

47

5 Arctic Stratus - Airborne Observations

As Arctic stratus exhibits a different type of cloud, their microphysical and optical inho-

mogeneities are expected to differ significantly from those of cirrus. To investigate these

inhomogeneities, fields of cloud optical thickness τst are retrieved from airborne upward ra-

diance measurements of Arctic stratus. The data were collected with AisaEAGLE during

the international field campaign VERDI, introduced in Sect. 5.1. The influence of the highly

variable surface albedo introduces significant uncertainties to Arctic stratus cloud retrievals

and has to be addressed. Based on airborne nadir reflectivity (γλ) measurements in the

visible spectral range, Sect. 5.2 provides a method to discriminate sea ice and open water

under cloudy conditions. In cloudy cases the transition of γλ from open water to sea ice is

horizontally smoothed. In general, clouds reduce γλ above bright surfaces in the vicinity of

open water, while γλ above open sea is enhanced. With the help of observations and 3D

radiative transfer simulations, this effect and its horizontal range is quantified in Sect. 5.4.

Furthermore, the influence of 3D radiative effects on the retrieved cloud optical properties

is investigated in Sect. 5.5. For selected cases with regard to the findings from Sect. 5.3 to

5.5, Sect. 5.6 presents then the retrieval of τst. Parts of this chapter have been published in

Schafer et al. (2015).

5.1 VERDI (VERtical Distribution of Ice in Arctic clouds)

The international Arctic field campaign VERDI took place in Inuvik, Northwest Territories,

Canada, in April and May 2012. The instruments (Tab. 5.1) were installed on Polar 5, an

aircraft used for scientific research by the Alfred Wegener Institute Helmholtz Centre for

Polar and Marine Research (AWI), Bremerhaven. During VERDI, Polar 5 was operated out

of the Inuvik Mike Zubko Airport. Consistent with the Arctic cloud climatolgy presented

by Shupe et al. (2011), the measurements during VERDI were characterized by persistent

Arctic stratus and less occurrence of high ice clouds. Most flights were performed over the

Beaufort Sea, partly covered by sea ice with open leads and polynias, which grew bigger

towards the end of the campaign. Figure 5.1 summarizes all flight tracks during the VERDI

campaign.

The measurement strategy during VERDI aimed at combining remote-sensing and in situ

cloud observations. Therefore, the same clouds were subsequently sampled by a set of in situ

(see Klingebiel et al., 2015) and remote-sensing instruments. The aircraft was equipped with

an active and several passive remote-sensing systems. The active system was the Airborne

Mobile Aerosol Lidar (AMALi; Stachlewska et al., 2010). It was operated in nadir viewing

direction at 532 nm wavelength. Passive radiation measurements were carried out with the

48 5. Arctic Stratus - Airborne Observations

Figure 5.1: Flight tracks performed during the VERDI campaign and true-color MODIS image(Aqua; 250m resolution) from 17 May 2012. Small inlet shows the location of the measurement areasituated in north-west Canada.

imaging spectrometer AisaEAGLE, to investigate cloud inhomogeneities and to analyze the

2D radiative effects of ice edges in a cloudy atmosphere. A 2x2 binning was used to increase

the frame rate to up to 30Hz. With the remaining 512 spatial pixels, the single-line sensor

provides a sufficiently high horizontal resolution to observe cloud inhomogeneities and ice

edges in detail. The flight altitude during the remote-sensing legs was about 3 km above

ground, which is about 2 km above cloud top for typical boundary layer clouds with cloud

top altitudes at about 1 km. For this geometry, the width of one AisaEAGLE pixel at cloud

top is 3.5m and the length is 4.2m at an exposure time of 10ms and a flight speed of 65m s−1.

Further passive radiation measurements were carried out with the Spectral Modular

Airborne Radiation measurement sysTem, initially designed for albedo measure-

ments (SMART-Albedometer; Wendisch et al., 2001), and a Sun tracking photometer

(Matsumoto et al., 1987). The SMART-Albedometer measures up-/downward spectral ra-

diance Iλ and irradiance Fλ (λ = 350–2100, 2–16 nm FWHM). The Sun photometer covers

aerosol optical thickness between λ = 367–1026 nm. The configuration was similar to that

during the aircraft campaign SoRPIC described by Bierwirth et al. (2013). Drop sondes were

used at selected waypoints to sample profiles of meteorological parameters (air pressure p,

air temperature T , relative humidity RH) needed for the radiative transfer simulations to

retrieve τst. Table 5.1 lists the instruments aboard Polar 5 and their relevant specifications.

The data from the AMALi and the drop sondes are used to determine the cloud-top altitude

and geometrical thickness. The data from the SMART-Albedometer are used to validate

the I↑λ measurements of AisaEAGLE. Furthermore, the SMART-Albedometer measurements

of the downward irradiance F ↓λ are used to transform the AisaEAGLE radiance I↑λ into the

5.2. Identification of Ice and Open Water 49

Table 5.1: Instrumentation of the Polar–5 aircraft during the VERDI campaign. Only those instru-ments are listed, which contributed to the data analysis within the scope of this thesis.

Instrument Measured Quantity Unit Range

AisaEAGLE Radiance Wm−2 nm−1 sr−1 λ=400–1000 nm

SMART - Radiance Wm−2 nm−1 sr−1 λ=350–2100 nmAlbedometer Irradiance Wm−2 nm−1 λ=350–2100 nm

AMALi Extinction Coefficient m−1 λ=355 nm, 532 nmCloud Top Altitude m z=0-3 km

CANON Camera RGB Radiance Wm−2 nm−1 sr−1 λ=(446,530,591) nm

Sun Photometer Aerosol Optical Depth – λ=367–1026 nm

AVAPS Lite - Air Pressure hPaDrop Sondes Temperature C

Relative Humidity %

nadir reflectivity γλ, which is a function of reff and τst (see Eq. (2.11)). The γλ are calculated

at a wavelength of 645 nm, where scattering is dominant and shows a significant sensitivity

to τst (Werner et al., 2013).

During all 15 flights throughout VERDI, 130 recordings (25 h, 11min, 29 s) of reflected

radiance from cloud-top and surface were collected with AisaEAGLE. 78% of the observation

time was spent above clouds. For 86% of the cloud observations a cloud retrieval as described

by Bierwirth et al. (2013) could not be applied as the surface albedo was high. Either snow-

covered ice almost eliminated the contrast between cloud and surface, or a mixture of ice

and open water made a cloud retrieval after Bierwirth et al. (2013) impossible. The latter

occurred in 42% of all observations and is analyzed in more detail to quantify the degree to

which cloud retrievals are biased above heterogeneous surfaces.

5.2 Identification of Ice and Open Water

A typical scene showing a mixture of sea ice and open ocean surfaces covered by an optically

thin stratus is presented in Fig. 5.2. The visible wavelength channels of the image provide

no visible contrast between sea ice and cloud. This is why near-infrared channels are applied

in MODIS cloud retrievals over sea ice. However, with AisaEAGLE the observations are

limited to wavelengths below 1000 nm, where the contrast is weak (compare Fig. 5.5) and

a retrieval of τst is not possible in those areas; it can only be performed above less reflecting

water surfaces.

The limitation of AisaEAGLE in the case of bright surfaces is illustrated in Fig. 5.3 showing

the calculated γλ at 645 nm wavelength for clouds with different values of τst over a dark

ocean surface (blue lines) and a bright sea-ice surface (red lines). The calculations were


Figure 5.2: VERDI flight track and true-color MODIS image (Aqua; 250m resolution) from 17May 2012. Numbers (1) and (2) label open ocean and sea ice, respectively.

performed for different solar zenith angles θ0 of 45, 60, and 75 (the range during VERDI

measurements).

The upper panel shows that the separation of γλ for clouds of different τst above sea ice

are not significant and far below the measurement uncertainties of most optical sensors.

Therefore, a retrieval of τst based on 645 nm reflectivity is not possible. For the same clouds

above a dark ocean surface, γλ is a strong function of τst, which is the basis of the cloud

retrieval following the method by Nakajima and King (1990), Bierwirth et al. (2013), and

Werner et al. (2013).

In order to select the dark-surface pixels for which a cloud retrieval is feasible, a sea-ice mask

has to be derived. Figure 5.3 clearly shows that even for optically thick clouds γλ is signifi-

cantly enhanced (≥ 25% at τst = 25 and θ0=60) above bright sea ice compared to a dark

ocean surface. This gap can be used as a threshold to distinguish between measurements of

clouds above the dark ocean surface and a bright sea ice surface. To define this threshold, it

has to be considered that the differences between γλ measured above a dark ocean surface

or a bright sea-ice surface is smaller for larger solar zenith angles and also decreases with

increasing τst (lower panel of Fig. 5.3). However, the differences are still significant at large

solar zenith angles of θ0=60 and τst = 25 (lower panel). For VERDI, where θ0 was in the

range of 55 to 75 for most of the observations, the particular threshold is defined as the

center value between the two simulations:

γλ,thresh =γλ,ice + γλ,water

2. (5.1)

To test this threshold, a section of a VERDI flight on 17 May 2012 (Fig. 5.2) was analyzed.

The flight was divided into a leg A at 2920m altitude above clouds (red in Fig. 5.2) and

a leg B inside the cloud at 150m altitude (blue in Fig. 5.2). The solar zenith angle was

5.3. Quantification of 3D Radiative Effects from Measurements 51

Figure 5.3: (a) Simulated γλ at 645 nm calculated for different τst ranging from 0 to 25 and cloudparticles with a fixed reff of 15 µm. The calculations were performed for different θ0 of 45, 60, and 75

over a highly reflecting ice surface and a dark ocean surface. (b) Difference between the simulatedγλ over bright sea ice surface and dark ocean surface from (a).

θ0=58. τst was obtained from AisaEAGLE measurements above open water far from the

ice edge using the retrieval method presented by Bierwirth et al. (2013). An average value

of τst = 5.3± 0.5 was derived, which agrees with the MODIS level-2 product showing values

for τst between 0.02 and 15.5 (τ st = 3.6 ± 2.5) in the investigated area. In that case, the

simulated γλ,ice = 0.8 and γλ,water = 0.2 from Fig. 5.3 give a threshold of γλ,thresh = 0.5.

Figure 5.4 shows a histogram of the measured γλ at 645 nm from leg A. There are two

distinctly separated maxima, which correspond to measurements above bright sea ice and

dark ocean. Either the minimum between the two maxima or the mean of those two most

frequent values of γλ can be used as an alternative estimate of the threshold for the ice

mask. In this particular case the threshold estimated from the frequency distribution is

γλ,thresh = 0.5, which confirms the theoretical value derived from the radiative transfer

simulations.

5.3 Quantification of 3D Radiative Effects from Measurements

Based on the thresholds, ice masks were created to identify measurements of clouds above

sea ice for which the cloud retrieval by Bierwirth et al. (2013) cannot be applied. Figure 5.5

shows three examples of γλ derived from the nadir radiance and zenith irradiance measure-

ments. Figures 5.5a and b show an extended ice edge, while Fig. 5.5c and d illustrate an

accumulated ice floe field, observed on 17 May 2012 around 17:00UTC (θ0=58). As ob-

tained from simultaneously performed AMALi measurements and data from the closest drop


Figure 5.4: Fraction of occurrence of the measured γλ at 645 nm, given in the example of Fig. 5.5a.The bin size is 0.01.

sonde (Fig. 5.6), in both cases a cloud layer with cloud top at 200m was observed between

the ground and the aircraft. Figures 5.5e and f show ice floes without cloud cover, observed

on 14 May 2012 at 21:00UTC. The corresponding ice masks are shown on the right panel in

Fig. 5.5. The pixels identified as sea ice are shown as red areas.

Figure 5.7 shows the frequency distributions for the three cases presented in Fig. 5.5 (solid

black lines). All frequency distributions are normalized so that the maximum is 1. In

each case, two maxima are separated by a distinct minimum, which defines the ice/water

threshold value. For the cloudy cases in Fig. 5.7a and b the dark-surface peak is broadened

asymmetrically towards higher γλ values, while the bright-surface peak is widened towards

lower γλ values. For the clear-sky case in Fig. 5.7c, the peaks representing dark ocean and

sea-ice surfaces are clearly separated.

To analyze the impact of the ice edge, frequency distributions for a selection of pixels far from

the ice edge are included in Fig. 5.7 for each particular scene, separated into dark open-water

pixels (dashed blue lines) and bright sea-ice pixels (dashed red lines). In Fig. 5.7a and b, the

peaks of the selective frequency distributions are much sharper than the original peaks. For

the clear-sky case in Fig. 5.7c, these selective frequency distributions are almost congruent

with the single peaks of the entire frequency distribution. This means that in this case the

ice edge has no impact on γλ of adjacent pixels, or in other words, there is no significant

horizontal photon transport. Between the selected pixels far from the ice edge and the pixels

directly over the ice edge are many pixels where γλ is enhanced (over open water) or reduced

(over sea ice) compared to the values at the remote pixels. This particular enhancement

and reduction of the measured γλ is most likely related to 3D radiative effects in clouds and

the reflection between clouds and the surface. This influence of the ice edge on the pixels’

reflectivity will most likely influence cloud retrievals based on 1D simulations in such scenes.

To clarify this hypothesis, in the following those 3D effects are investigated by analyzing

γλ with respect to the retrieved cloud optical properties. To characterize the magnitude


Figure 5.5: Left Side: Fields of γλ at 645 nm, measured with the imaging spectrometer AisaEAGLE.Right side: Same scenes as on the left side in color-scale and with ice mask overlay. The measurementswere performed on 17 May 2012 during the international field campaign VERDI and show (a), (b)an overpass over a straight ice edge during cloudy conditions, (c), (d) an overpass over scatteredice floes during cloudy conditions, and (e), (f) an overpass over larger ice floes during cloudlessconditions.

of the enhancement or reduction of the measured γλ, 3D radiative transfer simulations are

performed in Sect. 5.4 and used to identify the most important parameters that control 3D

effects. Afterwards, a 1D cloud retrieval is performed in Sect. 5.5 to quantify the influence

of the 3D effects on the retrieved τst and reff.

Figure 5.8 illustrates the measured γλ (solid lines) and its standard deviation (dotted lines)

as a function of the distance to the ice edge for the three scenes presented in Fig. 5.5. The

maximum values measured over sea ice and dark ocean water differ between the cloudy

and cloudless cases. This results from the different time of measurement and from the

different patterns of the hemispherical-directional reflectance function (HDRF), which can

be observed in nadir viewing direction over clouds and sea ice. In nadir viewing direction,

the HDRF of clouds shows a minimum and increases with increasing observation angle. In

contrast, the HDRF of sea ice shows approximately the same values for lower (nadir) and


Figure 5.6: (a) Flight altitude hAircraft (black) and cloud top altitude hcloud (green) derived fromAMALi measurements aboard Polar 5 on 17 May 2012 with 5 s temporal resolution and 7.5m verticalresolution. (b) Profiles of temperature T (red) and relative humidity RH measured with a drop sondelaunched at 16:59:40 UTC. Dotted lines serve as reference lines and mark the cloud top altitude ofhcloud =200m and the start time of the drop sonde.

larger (limb) observation angles (Ehrlich et al., 2012). Compared to cloudy cases, this results

in observations of larger γλ.

Furthermore, Fig. 5.8 shows that for the cloudy cases presented in Fig. 5.5a and c (red and

blue in Fig. 5.8), close to the detected sea ice areas, a slight enhancement of γλ was measured

over the open sea; while over the ice-covered area, γλ is reduced (indicated by arrows in

Fig. 5.8). This results most likely from 3D radiative effects in clouds and the interaction

between clouds and the surface. In this chapter, only the latter case is considered, namely,

the 3D radiative effects related to the pathway of the photons between cloud and surface.

Horizontal photon transport in the layer between surface and cloud smoothes the abrupt

decrease of the surface albedo from large values above sea ice to low values above the open

water. For measurements without clouds (Fig. 5.5f, green in Fig. 5.8) similar areas with

enhanced γλ above the water close to the ice edge were not found.

The hypothesis linking the 3D radiative effect to the enhancement of γλ is illustrated in

Fig. 5.9. The incident radiation (F0 · cos(θ)) impinges on the cloud, where scattering and

absorption processes take place. Part of the incident radiation is transmitted through the

cloud and scattered into the direction of the ice edge (bold black arrow). Sea ice acts

similarly to a Lambertian reflector and reflects the incoming radiation almost uniformly

in all directions (isotropic, gray arrows). The reflected radiation penetrates the cloud at

a certain altitude (red or blue arrows), where parts of it are scattered into the observation

direction. Without sea ice in the vicinity of the measurements, the reflected radiance would

be influenced only by the cloud and dark ocean water. With sea ice in the vicinity, the

measured nadir radiance I↑λ above the cloud parcel is enhanced due to the additional radiation

reflected by the sea ice into the direction of the last scattering point in the cloud. This

effect is significant only for cloudy cases, because of the weak scattering efficiency of the

clear atmosphere compared to that of clouds. Comparing this effect for clouds of different


Figure 5.7: Normalized distributions of the frequency of occurrence of γλ measured during the threecases presented in Fig. 5.5. Additionally included are the frequency distributions over sea ice anddark ocean water only.

altitude (Fig. 5.9), the horizontal photon path of the reflected radiation is extended for clouds

of higher altitude (compare for cloud A (red) and cloud B (blue)). Hence, the range of the

3D effect increases with cloud altitude.

For the case of the straight ice edge (Fig. 5.5a), the distances presented in Fig. 5.8 are almost

in line with the flight track, which was perpendicular to the ice edge. With a frame rate of

30Hz and an aircraft speed of 65m s−1 this results in 700 measurements along the 1418m

for each of the 512 spatial pixels. The mean γλ measured along the flight path is illustrated

as a solid red line in Fig. 5.8. In general, γλ decreases by about two thirds from γλ = 0.75

above bright sea ice to about γλ = 0.25 above dark ocean surface. The decrease does not

occur sharply at the ice edge, but gradually starts at about 400m distance from the ice

edge and ends at 400m distance from the ice edge over open water. In the cloudless case,

the asymptotic values above sea ice and water are reached much closer to the ice edge at

about 50m.

Two distances are defined relative to the ice edge to quantify the enhancement effect. The

first distance ∆LHPT is introduced to quantify the range of horizontal photon transport. It

characterizes the distance at which the transition from high γλ,ice to low γλ,water is 1/e3 of

the initial difference between the mean γλ above ice (γλ,ice) and the mean γλ above open

water (γλ,water):

γλ,water(∆LHPT) = γλ,water +1

e3·∆IPA, (5.2)

with ∆IPA = γλ,ice−γλ,water. The threshold of 1/e3 (≈ 5%) is chosen to make the results for

∆LHPT comparable to the second distance, which is introduced in the following and related to


Figure 5.8: Averaged γλ (solid lines) ±6% measurement uncertainty of γλ (dashed lines) at 645 nmwavelength, measured perpendicular to the ice edges shown in Fig. 5.5. Arrows indicate the particularenhancement or reduction of γλ close to the detected ice edges.

the AisaEAGLE measurement uncertainty. Since ∆LHPT is not related to the AisaEAGLE

measurement uncertainty, 1/e3 instead of 6% is chosen to avoid misunderstandings. By

including ∆IPA, ∆LHPT quantifies the range of horizontal photon transport independent

of the difference of the surface albedo contrast. For the scene from Fig. 5.5a (see red line

in Fig. 5.8), ∆LHPT indicated by the enhancement of γλ over the water surface extends to

a distance of 200m from the ice edge.

A second distance to the ice edge ∆L is defined for which γλ,water is enhanced by 6% of the

average γλ above open water.

γλ,water(∆L) = γλ,water + 0.06 · γλ,water. (5.3)

The choice of the threshold results from the radiance measurement uncertainty (±6%) of

the imaging spectrometer AisaEAGLE. Using this definition, ∆L is independent of γλ mea-

sured above the ice surface. It only accounts for the significance of the enhancement with

respect to the measurement uncertainty. If the enhancement is higher than the measurement

uncertainty, a cloud retrieval might be significantly biased. Therefore, ∆L is a measure for

the horizontal extent within which the 3D effects bias the cloud retrieval in the vicinity of

an ice edge. For the special case of the measured γλ in Fig. 5.8, ∆L = 300m. Above open

water, all measurements within that transition zone cannot be used for the cloud retrieval

as the enhanced γλ will increasingly bias the retrieved τst.

For the isolated ice floes of Fig. 5.5c, the values of the averaged γλ (solid blue line) in Fig. 5.8

are comparable to the values from the scenario in Fig. 5.5a. Furthermore, Fig. 5.8 shows

a similar analysis (solid green line) for the cloud-free scenario on 14 May 2012 (Fig. 5.5f).

5.4. Simulations 57

Figure 5.9: Sketch of the 3D radiative effects between clouds at two different altitudes and thesurface in the vicinity of an ice edge. The arrows illustrate the pathway of the photons betweensource, cloud, surface, and sensor.

Here, the decrease of γλ at the ice edge is significantly sharper than for the cloud-covered

scenes. This indicates that in the cloudy scenes horizontal photon transport is taking place

in the layer between the bright surface and cloud base, leading to a smoother transition

between bright sea ice and dark ocean water.

5.4 Simulations

5.4.1 3D Radiative Transfer Model

To analyze the observations of 3D radiative effects at ice edges, a 3D radiative transfer model

is applied. The simulations are used to determine ∆L and ∆LHPT as a function of different

cloud properties. It is expected that the interaction between clouds and sea-ice surface varies

with varying τst, geometrical thickness, and cloud altitude. Furthermore, the simulations are

used to clarify whether these 3D radiative effects result in an enhancement of the mean γλfor a certain area or if the enhancement is, on average, counterbalanced by the decrease of

γλ above the sea ice. Different idealized sea-ice geometries are studied.

The radiative transfer simulations of the upward radiance I↑λ and downward irradiance F ↓λ

to derive γλ are performed with the open-source Monte Carlo Atmospheric Radiative

Transfer Simulator (MCARaTS), which is a forward-propagating Monte Carlo photon-

transport model (Iwabuchi, 2006; Iwabuchi and Kobayashi, 2008). It traces individual pho-

tons on their path through the 3D atmosphere. To reduce the computational effort for radi-

ance simulations, MCARaTS uses several variance-reduction techniques, such as a modified


local-estimate method or a truncation approximation for highly anisotropic phase functions

(Iwabuchi, 2006). The input for the radiative transfer model contains the optical properties

of clouds, aerosol particles, trace gases (e.g. extinction coefficient, single-scattering albedo,

phase function), and the 2D surface albedo. An albedo field of 20 km by 20 km with a pixel

size of 50m by 50m (400 pixels in both horizontal dimensions) is created. Depending on

the given sea-ice distribution, the albedo of individual pixels is set to 0.910 at 645 nm for

sea ice or 0.042 at 645 nm for dark ocean water (Bowker et al., 1985). The pixel size of

the 3D model is about ten times larger than that of AisaEAGLE. However, model results

and measurements are still comparable as the investigated 3D effects occur in the range of

a few hundred meters on either side of the ice edge. Accordingly, the AisaEAGLE data are

averaged for comparing the model results with the measurements. 2.2 × 109 photons were

used in each single model run, which resulted in a noise level of the 3D simulations of less

than 1%. This value is much lower than the measurement uncertainties of AisaEAGLE.

Other input parameters for the model are adapted to the measurement conditions on 17

May 2012 around 17:00UTC with a solar zenith angle of θ0=58 and the solar azimuth

angle of φ0=113. The extraterrestrial solar spectrum was taken from Gueymard (2004).

The output altitude for I↑λ and F ↓λ is 2920m (10 000 ft flight altitude). With regard to the

measured scenes (Fig. 5.5a and c), a horizontally and vertically homogeneous liquid water

cloud was assumed between 0 and 200m altitude. Besides reference simulations for clear-sky

conditions, the cloud optical thickness was varied between τst = 1 and τst = 10 as observed

by MODIS in the surroundings of the measurement area. Based on in situ observations

(Cloud Droplet Probe, CDP, Klingebiel et al., 2015), the effective radius of the liquid water

droplets was set to reff=15 µm. The microphysical properties of the liquid water clouds are

converted to optical properties by Mie calculations. Furthermore, profiles of the atmospheric

pressure, temperature, density, and gases are taken from Anderson et al. (1986). Gas absorp-

tion was modelled by LOWTRAN (Low Resolution Transmission Model parameterization,

Pierluissi and Peng, 1985), as adapted from SBDART (Santa Barbara DISORT Atmospheric

Radiative Transfer, Ricchiazzi and Gautier, 1998).

Additionally, 1D simulations, which use the independent pixel approximation (IPA), are

applied to the particular cases. The IPA simulations were performed with the same 3D

model, but with a homogeneous surface albedo – either dark ocean water or bright sea ice.

All other parameters remain the same as in the 3D simulations.

5.4.2 Case I: Infinitely Straight Ice Edge

An infinitely straight ice edge comparable to Fig. 5.5a is assumed. Figure 5.10 illustrates

the results of the 1D (gray lines) and 3D (black lines) cases. Similar to the observations,

γλ from the 3D simulations decreases above the bright sea ice, and increases above the dark

ocean surface. The effect is larger the closer the pixel is located to the ice edge. In the

clear-sky simulations this effect is small; 3D and IPA simulations are almost identical. This

indicates that the 3D effect is dominated by horizontal photon transport between sea ice

and clouds and the scattering processes by the cloud particles into the nadir observation

direction. Without clouds, the horizontal photon transport above the isotropically reflecting

5.4. Simulations 59

surface is of similar magnitude to the cloudy case. However, due to the weak scattering in the

clear atmosphere compared to the scattering by cloud particles, this effect is only significant

for cloudy cases.

Similar investigations are presented by Marshak et al. (2008) with respect to aerosol-cloud

interactions. In the vicinity of clouds, they found that the radiance in cloudless columns

is increased due to a cloud-induced enhancement of the Rayleigh scattering. In general,

Fig. 5.10 shows that with increasing τst the slope of the decrease of γλ next to the ice edge

is flattened. This is a result of the reduction in contrast between the dark ocean surface and

bright sea-ice surface by the overlying clouds.

Figure 5.10: Simulated mean γλ across an ice edge for clear-sky conditions as well as for low-levelclouds between 0 and 200m altitude, τst = 1/5/10, and reff =15 µm. The white area illustrates thebright sea ice, the gray area the dark ocean water. Included are the results of the 3D and IPAsimulations, as well as the average of γλ, measured perpendicular to the ice edge in Fig. 5.5a.

To compare the results with the measurement example in Fig. 5.8, the distance ∆LHPT

defined by Eq. (5.2) is analyzed. The results are summarized in Tab. 5.2. γλ,water is set

to the IPA values above water. For the cases presented in Fig. 5.10, ∆LHPT increases with

increasing τst from 100m at τst = 1 to 250m at τst = 5 and to 300m at τst = 10. This shows

that the horizontal photon transport increases with τst due to increased scattering inside the

cloud layer.

In contrast to ∆LHPT, the distance ∆L (see Tab. 5.2) defined by Eq. (5.3) decreases from

600m (at τst = 1.0) to 400m (at τst = 5.0) and to 250m (at τst = 10.0). The decrease of

∆L suggests that the area in which γλ is enhanced and a cloud retrieval might be biased is

smaller for optically thick clouds. This is related to the decrease in contrast between cloud

covered sea ice and cloud covered ocean if τst increases. The difference ∆(IPA) between γλ,iceand γλ,water decreases from γλ = 0.87 for the clear-sky case to γλ = 0.44 for τst = 10, mainly

due to the increasing reflection of incoming radiation by the cloud. If τst increases, γλ,water


increases, which results in a higher uncertainty range exceeding the γλ enhancement also

in areas closer to the ice edge. Therefore, the γλ enhancement becomes less significant for

a cloud retrieval compared to the measurement uncertainties. Since the aim is to retrieve

τst above water areas enclosed by ice floes, in the following ∆L is used to quantify the 3D

effects.

Additionally, the sensitivity of the results to the assumption of a constant reff was analyzed

by running simulations with an reff of 10, 15, 20, and 30 µm (see Tab. 5.2). The results

showed that ∆L is almost independent of reff. This indicates that a variation of reff does not

need to be considered when estimating the 3D radiative effects described here.

Furthermore, simulations with variable values of the surface albedo were performed (see

Tab. 5.2). Based on the measurement uncertainty of AisaEAGLE, the surface albedo of the

dark ocean water and bright sea ice was varied by ± 6%. Over the dark ocean area, the

simulations show almost identical results with differences far below 1% in γλ. Compared to

the measurement uncertainties, those differences in the surface albedo are of less significance

for ∆L. Indeed, the albedo has a larger effect over the sea-ice surface (up to 10%) due to the

relative albedo change of 6%, which corresponds to an absolute change of ±0.05 compared

to 0.002 absolute change for the water surface. For the investigations presented here, the

effect over the dark ocean area is relevant only.

Figure 5.11: Simulated γλ for clouds at different altitudes and with different geometrical thicknessfor the passage from a highly reflecting ice-covered region to a darker region of open water. The whitearea illustrates the ice stripe. (a) Simulations for varying cloud base, given a fixed cloud geometricalthickness of 500m. (b) Simulations for varying cloud geometrical thickness, given a fixed cloud baseat 0m.

Other important aspects, which influence the results, are the cloud altitude and cloud geomet-

rical thickness. The horizontal photon transport resulting from the horizontal displacement

of the location where a photon is isotropically scattered at the surface and the location in the

cloud where it is scattered afterwards into the viewing direction, changes if the cloud geom-

etry changes. Figure 5.11 shows the simulated γλ for clouds of different altitude (Fig. 5.11a)

and clouds of different geometrical thickness (Fig. 5.11b). Table 5.2 lists the corresponding

5.4. Simulations 61

∆L. Increasing the cloud base of a cloud with a geometrical thickness of 500m and τst = 1

from hcloud = 0m to hcloud=1500m, ∆L increases from 1000 to 4000m. For τst=5, ∆L

increases from 800 to 3200m. Similarly, ∆L increases with increasing geometrical thickness.

For τst = 1, ∆L increases from 500 to 2200m when the cloud geometrical thickness changes

from 200 to 1500m. For τst=5, ∆L increases from 300 to 2000m. Compared to the influence

of τst, the cloud altitude and cloud geometrical thickness have a similar impact on ∆L and

cannot be neglected.

Figure 5.12: (a) Distance ∆L as a function of the cloud base altitude hcloud for a cloud witha geometrical thickness of ∆hcloud = 500m and different τst. (b) Distance ∆L as a function ofthe cloud geometrical thickness ∆hcloud for a low-level cloud with cloud base at hcloud = 0m anddifferent τst.

For two model clouds with a geometrical thickness of 500m and values of τst = 1 and τst = 5,

Fig. 5.12a shows ∆L as a function of the cloud base altitude hcloud. Similarly, Fig. 5.12b

shows ∆L as a function of the cloud geometrical thickness ∆hcloud for low-level clouds with

τst = 1 and τst = 5 and cloud base at 0m. The increase of ∆L with increasing altitude of

the cloud base (Fig. 5.12a) follows an almost linear function and can be parameterized by

∆L(hcloud, τst) = Ah(τst) · hcloud +Bh(τst). (5.4)

For the parameters Ah(τst) and Bh(τst), the linear regression yields Ah(τst)= 2.00/1.6 and

Bh(τst)= 1000m/800m for clouds with τst=1/5. This shows that the influence on ∆L is

much larger for clouds at higher altitudes and lower τst. Comparing the results for τst=1 and

τst=5 indicates that slope A decreases with increasing τst. This proves that the influence of

cloud geometry on ∆L is decreasing with increasing τst.

Similarly, ∆L increases almost linearly with increasing cloud geometrical thickness ∆hcloud.

This relation can be parameterized by

∆L(∆hcloud, τst) = A∆h(τst) ·∆hcloud +B∆h(τst). (5.5)


Table 5.2: Summarized distances ∆L and ∆LHPT of the presented case studies.

Cloud Optical Thickness τst 1 5 10

∆LHPT (hcloud=0–200m, reff = 15 µm) [m] 100 250 300∆L (hcloud=0–200m, reff = 15 µm) [m] 600 400 250

Effective Radius reff [µm] 10 15 20 30

∆L (τst = 1, hcloud=0–200m) [m] 600 600 600 600∆L (τst = 5, hcloud=0–200m) [m] 400 400 400 400

Surface Albedo α +6% -6%

∆L (τst = 1, reff = 15 µm, hcloud=0–200m) [m] 600 600∆L (τst = 5, reff = 15 µm, hcloud=0–200m) [m] 400 400

Cloud Base Altitude [m] 0–500 500–1000 1000–1500 1500–2000

∆L (τst = 1) [m] 1000 2000 3000 4000∆L (τst = 5) [m] 800 1600 2400 3200

Cloud Geometrical Thickness [m] 0–200 0–500 0–1000 0–1500

∆L (τst = 1) [m] 500 1000 1600 2200∆L (τst = 5) [m] 300 800 1400 2000

The regression of the increase of ∆L with increasing cloud geometrical thickness yields

A∆h(τst)= 1.3/1.3 and B∆h(τst)= 300m/100m for clouds with τst=1/5.

The cloud bases of all boundary layer clouds observed during VERDI ranged between 0

and 650m, which is in agreement with the climatology presented by Shupe et al. (2011).

To demonstrate the potential effects of clouds with higher cloud base, the following simula-

tions cover two cloud cases, one similar to the observed cases from Fig. 5.5a–d with a cloud

altitude of hcloud=0–200m and one with a cloud base at 500m and a cloud top at 1000m.

5.4.3 Case II: Single Circular Ice Floes

An infinitely straight ice edge as discussed in Sect. 5.4.2 does not represent reality in all

aspects. Often, scattered ice floes of different size are observed (see Fig. 5.5c). In this case,

a reduced 3D effect above open water due to the curvature of the ice edge is expected.

To analyze and quantify this reduction of 3D radiative effects, single circular ice floes of

different size are simulated. The radius of the circular ice floe was varied from 100 to 1000m

in steps of 100m and from 1 to 9 km in steps of 1 km. The center of the circular ice floe was

placed in the middle of the model domain. For reasons of symmetry, a cross section through

5.4. Simulations 63

the center of the model domain was used for the data evaluation. Figure 5.13 shows the

influence of the ice-floe size on ∆L.

As expected, ∆L is lower for small ice floe radii with larger curvature compared to the

infinitely straight ice edge simulated in Sect. 5.4.2. For the assumed values of τst, ∆L

increases with an increasing radius of the ice floe, asymptotically reaching a maximum value,

which is identical to the results of the infinitely straight ice edge (r = ∞). This shows that

all ice floes larger than about 6 km can be treated like the infinitely straight ice edge (for the

given cloud and observation geometry).

Figure 5.13: Simulations (gray and black lines) and parameterizations (red lines) of ∆L as a functionof the ice-floe size, different τst, and different cloud altitudes. Asymptotic maximum values of ∆L aremarked with dotted blue lines.

The reduction of ∆L for smaller ice floes can be explained by two effects. For ice floes with

radii smaller than the distance ∆L of the infinitely straight ice edge, rfloe < ∆L(τst), the size

of the ice area is too small for the γλ above the ice to reach the IPA γλ at any place. All

areas of the ice floe are affected by 3D effects. On the other hand, the area of the ice floe is

too small to fully affect the adjacent water area. The water area behind the ice floe limits

its effect. For ice floes with a radius larger than ∆L, the IPA γλ will be reached at some

point on the ice floe. Only the curvature of the floe reduces the 3D effect above open water.

For any water point near the ice edge, the ice area located close to this point is reduced with

increasing curvature. The curvature affects both small and large ice floes and lowers the 3D

radiative effects slightly until the maximum effect, which is reached for an infinitely straight

ice edge.

Combining these two effects and assuming an exponential relationship between ∆L and the

ice-floe size rfloe (with regard to the shape of the lines in Fig. 5.13), the results presented in

Fig. 5.13 are parameterized by:

∆L = ∆Lmax(τst) ·[1− 1

3· exp

(− rfloe∆Lmax(τst)

)− 2

3· exp

(−r2floeC2

)]. (5.6)


The distances for the infinitely straight ice edge, ∆Lmax(τst), are taken from Sect. 5.4.2. For

the exponential parameter C, the fit yields C = 1000m for clouds with τst = 1/5/10. The

parameterization is valid for ice floes with radii rfloe larger than 300m. For those ice floes,

the uncertainty is less than 5%. For ice floes with radii rfloe less than 300m, the uncertainty

increases rapidly and reaches up to 100%. This is due to the insufficient representation of

the circular shape of the small ice floes by squared pixels with 50m side length.

5.4.4 Case III: Groups of Ice Floes

In a next step, ice floes of different size have to be considered. The size of the ice floes, their

shape and the distance to each other influence the 3D effects. To address these cases, four

simulations with the same model setup as in Sects. 5.4.2 and 5.4.3, but with changed shape

and number of the ice floes are performed. In total, four scenarios with ice floes represented

by squares (total sea-ice area Ax, total ice-edge length lx) were investigated to quantify the

influence of Ax and lx on the 3D effects.

In Scenario 1 (reference), an ice floe with a size of 5 km by 5 km (A1=25 km2, l1=20 km)

was placed in the center of the model domain (Fig. 5.14a). For Scenario 2 (Fig. 5.14b), the

total sea-ice area was conserved (A2 = A1 = 25 km2), however, the total ice-edge length was

doubled (l2=2 · l1=40 km). This was realized by four smaller ice floes (2.5 km by 2.5 km),

separated by a distance of 5 km from each other. Scenario 3 (Fig. 5.14c) simulates two

small ice floes (2.5 km by 2.5 km) for which the total ice-edge length has been conserved

(A3 = 0.5 · A1 = 12.5 km2, l3 = l1 = 20 km). Scenario 4 (Fig. 5.14d) was designed

to investigate the effect of the distance between the single ice floes. The two ice floes of

Scenario 3 (A4 = 0.5 · A1 = 12.5 km2, l4 = l1 = 20 km) were copied, but placed next to

each other.

As expected, in each scenario the contrast at the ice floe boundaries is reduced due to the

3D effects. To quantify the 3D radiative effect in the entire model domain, average and

standard deviation of γλ are calculated separately for the total domain, for sea-ice areas, and

for dark ocean areas (see Tab. 5.3). The average γλ is largest for Scenario 1 and smallest

for Scenarios 3 and 4. This is not surprising since the area of the ice floes in Scenario 3

and 4 is half the area of the reference scenario. Compared to the IPA results, evidence of

the 3D radiative effect is found in a slight reduction of the average γλ in all scenarios. This

reduction originates from the absorption of the radiation that is scattered by the cloud base

back into the direction of the dark ocean surface. This part of absorption is not considered

in the IPA simulations, which leads to a lower scene average reflection in the 3D simulations.

The standard deviations in the 3D simulations are also lower than in the IPA results, which

corresponds to the smoothing at the ice edges. Furthermore, Tab. 5.3 reveals that the

magnitude of γλ,water and γλ,ice is a function of the ratio between the sea-ice area and ice-

edge length (A/l). With increasing ratio A/l, γλ,water decreases and γλ,ice increases. This is

related to the lower probability that the sea-ice surface is directly connected to the dark ocean

surface. Regarding γλ,total, no significant influence of A/l is found. Here, the magnitude of

γλ,total is mainly a function of the total sea-ice area compared to the total dark ocean area.

5.4. Simulations 65

Figure 5.14: Ratio R3D/IPA of γλ of the 3D and IPA simulation at τst = 5 and for a cloud between500 and 1000m altitude. Each panel displays one of the four scenarios.

To quantify the 3D radiative effects, the ratios R3D/IPA= γλ,3D/γλ,IPA of the derived γλfrom the 3D and IPA simulations are calculated. If both simulations are equal, the ratio

is R3D/IPA = 1. Compared to the IPA simulations, a ratio of R3D/IPA > 1 represents an

enhancement of γλ. Table 5.4 lists R3D/IPA for all simulated τst and hcloud. Figure 5.14

displays the R3D/IPA for a cloud with τst = 5 at hcloud = 500–1000m, since the 3D effects are

more evident for larger τst and higher cloud altitudes. Yet, the overall 3D effect is relatively

small with R3D/IPA ranging from 0.965 to 0.984, but is still significantly higher than the noise

level of the 3D simulations. The small values are caused by the large model domain and the

relatively small ice fraction. Most pixels are ice-free and at a distance to the ice floes where

3D effects are negligible.

In Scenarios 1–3, the individual ice floes do not affect each other, as the distance between

them is too large. Here, similar 3D effects are observed. The corners of the ice floes are

smoothed out and the γλ field around the ice floe becomes more circular. This results in

larger ∆L values at the center of the ice edges and in smaller ∆L values close to the corners.

For the large ice floe of Scenario 1, ∆L = 1400m at the center of each side. In agreement

with Fig. 5.13, ∆L for the small ice floes in Scenarios 2 and 3 is smaller (1200m). Along the

normal line of the corners, ∆L is reduced to 900m for Scenario 1 and 700m for Scenarios 2

and 3. In Scenario 4, the ice floes cause a different pattern close to their point of contact.

Here, ∆L is largest measured tangential to the connected corners and reaches 2000m as the

3D radiative effects of both floes add up for these points.


Table 5.3: Average and standard deviation of the simulated γλ from the four presented scenarios forthe whole surface albedo field (γλ,total), ice covered areas only (γλ,ice), and water covered areas only(γλ,water). Simulations performed for clouds with an optical thickness of τst =1 and τst =5.

Simulation Scenario γλ,total γλ,ice γλ,water3D, τst = 1 1 0.122± 0.171 0.782± 0.045 0.077± 0.012

2 0.122± 0.163 0.737± 0.045 0.081± 0.0203 0.098± 0.118 0.737± 0.045 0.077± 0.0124 0.098± 0.118 0.741± 0.045 0.081± 0.024

IPA, τst = 1 1 0.126± 0.200 0.896 0.0732 0.126± 0.200 0.896 0.0733 0.102± 0.147 0.896 0.0734 0.102± 0.147 0.896 0.073

3D, τst = 5 1 0.274± 0.105 0.654± 0.081 0.250± 0.0242 0.270± 0.081 0.561± 0.065 0.254± 0.0283 0.254± 0.061 0.561± 0.065 0.250± 0.0204 0.254± 0.061 0.569± 0.065 0.250± 0.024

IPA, τst = 5 1 0.279± 0.145 0.844 0.2412 0.279± 0.145 0.844 0.2413 0.258± 0.105 0.844 0.2414 0.258± 0.105 0.844 0.241

Fig. 5.15 shows frequency distributions of γλ for the four scenarios. Since the clouds are

homogeneous in the simulations, the γλ in areas unaffected by 3D effects are identical to the

γλ from the IPA simulation. For the open-water pixels, this causes a single peak at γλ(τst =

5) = 0.24. For pixels above ice, no single peak corresponding to the IPA γλ(τst = 5) = 0.84

is observed. This is due to the small size of the ice floes, above which the IPA γλ is not

reached. All γλ values that are not included in the single water peak result from the 3D

effects. Above ice, the distributions of Scenarios 2–4 are shifted to lower γλ compared to

Scenario 1. This is because the diameter of the floes is even smaller than in Scenario 1.

Thus, the large reflectivity values of Scenario 1 are not reached by Scenarios 2–4 (compare

Fig. 5.13). Comparing the frequency distribution of Scenarios 1 and 2, Fig. 5.15a reveals the

effect of the increased ice-edge length in Scenario 2. More pixels are affected by 3D effects

and show values different from IPA. Furthermore, with four times the number of corners in

Scenario 2, γλ above water is slightly shifted to lower values compared to the reference case.

Similar effects can be observed in Scenario 3. In Scenario 4, the combined effect of both floes

leads to larger enhancements above ocean water than in Scenarios 2 and 3. In comparison

to Scenario 3, the reduced distance between the ice floes in Scenario 4 leads to a shift of the

frequency distribution over water to larger γλ values. Similar results can be observed for the

frequency distribution over ice.

In order to identify the relevant effects, the ratios R3D/IPA for ice-free (Rwater) and ice-

covered (Rice) areas are calculated separately (Tab. 5.4). The reduction of γλ above ice

5.4. Simulations 67

Table 5.4: Ratio R3D/IPA of γλ for the total scene area (Rtotal), for the sea-ice covered area (Rice), andfor the dark ocean covered area (Rwater) of all scenarios from Sects. 5.4.4 and 5.4.5. The simulationsfor Scenario 1–4 are performed with clouds of τst = 1 and τst = 5 at an altitude of 0–200 and500–1000m. The simulation for the real case is performed with a cloud of τst = 5 at an altitude of100–200m.

0–200m τst = 1 τst = 5Scenario Rtotal Rice Rwater Rtotal Rice Rwater

1 0.997 0.961 1.030 0.995 0.951 1.0072 0.991 0.941 1.043 0.991 0.917 1.0163 1.000 0.940 1.030 0.995 0.917 1.0074 1.001 0.942 1.048 0.995 0.918 1.012Real Case – – – 0.926 0.732 1.240

500–1000m τst = 1 τst = 5Scenario Rtotal Rice Rwater Rtotal Rice Rwater

1 0.974 0.875 1.072 0.974 0.775 1.0322 0.965 0.825 1.128 0.965 0.665 1.0603 0.984 0.823 1.067 0.979 0.665 1.0284 0.984 0.829 1.094 0.981 0.675 1.039

is larger (Rice = 0.823–0.875) than the enhancement above water (Rwater = 1.072–1.128),

which is partly a result of the larger water area. The small size of the ice floes leads to the

stronger effects above sea ice, as the IPA γλ is not reached. Interestingly, with increasing

τst, the deviations from IPA increase for the ice area but decrease for the dark ocean area.

This effect is related to the asymmetry of enhancement and reduction for clouds of high τst,

as shown in Fig. 5.10.

The average reduction over sea–ice areas (Rice) is largest for Scenario 1. For all other sce-

narios, smaller values are obtained, with Scenarios 2 and 3 showing identical values. This

indicates that the particular distance between the ice floes in Scenarios 2 and 3 is large

enough to suppress influence of the single ice floes on each other. Scenario 4 gives the second

largest Rice. Compared to Scenario 1 and Scenario 3, this confirms that the distance between

the ice floes has a significant influence on the enhancement of γλ over dark ocean water in

the vicinity of ice edges.

Rwater is almost equal for Scenarios 1 and 3, although the ice-covered area differs by a factor

of two. For Scenario 2, with a doubled ice-edge length, this ratio is significantly larger.

This leads to the conclusion that the ice-edge length has a significantly larger effect on the

enhancement of γλ (over the water next to an ice edge) than the size of the area covered by

sea ice.

5.4.5 Case IV: Realistic Sea-Ice Scenario

In order to combine several aspects of the 3D effects, γλ was simulated above an albedo field

generated from the observation shown in Fig. 5.5c. The pixel size of the albedo map was


Figure 5.15: Single logarithmic frequency distributions of the simulated γλ from all four scenariosdisplayed in Fig. 5.14.

adjusted to the pixel number and size of the AisaEAGLE measurements (488 by 601 pixels

with 5m pixel side length).

The albedo map was used in the simulations implementing a cloud of τst=5 and a fixed

reff=15 µm, as derived from in situ measurements. With regard to the measurements of the

AMALi aboard Polar 5 and the closest drop sonde (see Fig. 5.6), the cloud top altitude was

set to 200m.

The best agreement between measurement and simulation is derived for this specific case

for a cloud base altitude of 100m and a slightly adjusted surface albedo (αwater = 0.09,

αice = 0.83). Figure 5.16 shows the frequency distributions of simulated and observed γλ.

The maxima of the ocean-water and sea-ice peaks are found at equal γλ. In regions over

dark ocean water as well as over bright sea ice, the γλ of the observation show a broader

distribution than the γλ of the simulation. Indeed, the magnitude of the simulated γλ peak

above the sea-ice surface agrees well with the peak from the observation, while the difference

above the dark ocean water is larger. The different magnitude and the broader distribution

of the observed single peaks compared to the simulation result from simplifications in the

simulations where a horizontally homogeneous cloud is assumed. Thus, variations of γλ due

to cloud 3D effects are not included here. Only the surface 3D effects cause a broadening of

the frequency distribution. However, while surface effects will fill up the gap between the two

peaks only, cloud inhomogeneities can also result in values smaller (over water) and higher

(over sea ice) than the IPA simulations.

Table 5.4 shows the ratios R3D/IPA between the results of the 3D and IPA simulation for the

realistic sea-ice scenario. Compared to the idealized scenarios in Sect. 5.4.4, for the realistic

sea-ice scenario the differences between the IPA and 3D simulations are larger above dark

ocean water and smaller above bright sea ice. This behavior is related to the larger sea-ice

fraction in the realistic sea-ice distribution, where water pixels are surrounded by a larger ice

5.5. Sensitivity of τst and reff derived from Synthetic Cloud Retrieval 69

Figure 5.16: Frequency distributions of measurement and simulation. 3D simulation performed forthe second measurement case, presented in Fig. 5.5 and Sect. 5.2. The bin size in γλ is 0.005.

area compared to the isolated sea-ice floes of Sect. 5.4.4. On the one hand, it shows that the

main characteristics of the ice-edge induced 3D radiative effects in clouds can be studied by

using idealized surface albedo fields. On the other hand, in case of a real sea-ice distribution

from measurements, it is also necessary to consider the real surface-albedo distribution for

deriving ∆L and the overestimation in the retrieved τst and reff. No fixed values for ∆L or the

overestimation can be given as a function of τst and cloud altitude only. The surface-albedo

distribution plays a major role as well and has to be known.

5.5 Sensitivity of τst and reff derived from Synthetic Cloud

Retrieval

All simulations in Sect. 5.4 showed that γλ over open water areas close to sea ice is enhanced

if clouds are present. For a cloud retrieval following the strategy by Bierwirth et al. (2013),

this enhancement suggests that τst will be overestimated in this area when a surface albedo

of water is assumed. To quantify the magnitude of this overestimation, a synthetic cloud

retrieval is investigated. It is based on simulations to investigate the uncertainties of retrieved

reff, which cannot be derived from the current setup of AisaEAGLE measurements during

VERDI. The limitation of AisaEAGLE to visible wavelengths restricts the retrieval to τst(Bierwirth et al., 2013). However, near-infrared measurements might be available by use of

additional imaging spectrometers. Therefore, this study addresses both quantities τst and

reff.

The retrieval based on the best fit to the forward simulations is applied to the γλ field of

a 3D simulation where the cloud optical properties are predetermined. An isolated ice floe

with a radius of 6 km (Sect. 5.4.3) is chosen and a homogeneous cloud with τst = 10 and

reff=15 µm is placed above it at an altitude of 500 to 1000m. With a radius of 6 km the ice


floe has an effect similar to that of an infinitely straight ice edge, which leads to the maximum

range of 3D effects with the largest ∆L (see Fig. 5.13). The retrieval is performed over the

dark ocean surface. The forward simulations of the γλ LUT are based on 1D simulations.

τst and reff are varied in the range of 1–25 and 10–25 µm, respectively; see Fig. 5.17. The

retrieval grid is constructed from the simulated γλ at 645 nm wavelength on the abscissa

and the ratio of γλ at 1525 and 579 nm wavelength on the ordinate. This wavelength and

the wavelength ratio is chosen in order to improve the retrieval method by Bierwirth et al.

(2013).

The choice of wavelength follows the method presented by Werner et al. (2013). This method

creates a retrieval grid with a more separated solution space for τst and reff than the classic

two-wavelength method by Nakajima and King (1990) or Bierwirth et al. (2013). Further-

more, it effectively corrects the retrieval results for the influence of overlying cirrus and

reduces the retrieval error for τst and reff caused by calibration uncertainties (Werner et al.,

2013). For airborne investigations of τst and reff with large spatial coverage and high spatial

resolution, this results in a higher accuracy of the retrieved cloud properties.

Figure 5.17: Retrieval grid using γλ at 645 nm and the ratio of γλ at λ1/λ2 = 1525 nm/579 nm. γλof the 3D simulation are illustrated by color-coded dots as a function of distance to the ice-floe edge.The black cross marks the exact cloud properties τst = 10 and reff =15 µm used in the 3D simulationfor the cloud at 500 to 1000m altitude.

The γλ of the 3D simulation is plotted in Fig. 5.17 as dots color-coded with the distance to

the ice edge. The exact result of a cloud with τst = 10 and reff=15 µm is marked with a black

cross. The results imply a significant overestimation of τst and reff at distances below 2 km

from the ice edge (dark blue dots). The overestimation increases with decreasing distance to

the ice edge. As expected, for distances larger than 2 km from the ice edge (light blue to red

dots) the γλ is close to the IPA value (black cross). Small deviations are results of noise in

the 3D simulations. For the range below ∆L = 2km, the mean τst and reff (solid lines) and

their standard deviation (dotted lines) derived from the retrieval are shown as a function of

the distance to the ice edge in Fig. 5.18.

5.6. Cloud Optical Thickness Retrieval 71

The graph shows that the overestimation of τst increases to up to 90% while reff is biased

by up to 30% close to the ice edge. Both values are valid only for the cloud used in the

simulations (τst=10 and reff=15 µm). For a smaller τst, the effect will be reduced. Further-

more, Fig. 5.18 shows that the overestimation of τst increases approximately exponentially

starting at about 1.5 km distance, while the overestimation of reff increases more slowly and

only reaches up to a distance of 1.0 km.

Figure 5.18: Overestimation (average and standard deviation) of τst and reff as a function of thedistance to the edge of the ice floe. The model cloud at an altitude of 500 to 1000m had τst = 10and reff =15 µm.

This indicates that the magnitude of the 3D effects depends on the wavelength. In all

simulations shown in Sect. 5.4.1, a wavelength of 645 nm is used for the retrieval of τst.

However, the retrieval of reff also requires simulations at 1525 nm in the absorption band of

liquid water. Therefore, the smaller magnitude and horizontal extent of the overestimation

of reff compared to the magnitude and horizontal extent of the overestimation of τst suggest

that the 3D effects will be smaller at absorbing wavelengths.

5.6 Cloud Optical Thickness Retrieval

With respect to the retrieval uncertainties caused by ice surfaces as discussed in Sect. 5.5,

the following retrievals of τst are only performed over areas covered by dark ocean water and

for a sufficiently large distance to the ice edges (larger than ∆L, as estimated from cloud

geometry and first guess of τst). From all flights, conducted during VERDI, ten segments

(4 to 26 km long) of AisaEAGLE measurements are chosen, which allow a retrieval of τst.

As the AisaEAGLE imaging spectrometer is restricted to measurements in the visible wave-

length range only, the reff is provided by the retrieval using the measurements of the SMART-

Albedometer. Similar to the synthetic cloud retrieval presented in Sect. 5.5, radiance mea-

sured by SMART at wavelength of 645 nm and 1 525 nm are used to retrieve reff here. By the

SMART–Albedometer, the reff is retrieved in nadir viewing direction only. For the retrieval


of τst using AisaEAGLE, reff is assumed to be constant along the swath (all 488 spatial pixels

in one line). Thus, variations of reff are only considered along the flight path. Uncertainties

arising from a constant reff along the swath were quantified by Bierwirth et al. (2013) to be

in a range less than the measurement uncertainty.

The measured fields of I↑λ are interpolated to LUT of simulated I↑λ, obtained from libRadtran

(Mayer, 2005). In comparison to the simulations for the CARRIBA campaign in Sect. 4.2,

the radiative transfer calculations are initialized to represent the environmental parameters

during the particular measurements. The relative geometry of the Sun and the observa-

tion geometry from the aircraft are obtained from the corresponding measurement time

and a GPS/INS (Global Positioning and Inertial Navigation System) unit. The cloud-top

altitude is obtained from AMALi measurements. The aerosol optical thickness (τaer) was

observed by a Sun photometer on board of Polar 5. The OPAC Arctic aerosol type (Optical

Properties of Aerosols and Clouds; Hess et al., 1998) is assumed in the calculations. The

profiles of atmospheric gases are provided by libRadtran (subarctic winter; Anderson et al.,

1986) and adapted by drop sonde profiles of T , p, and RH. A continuous transition from the

standard to the drop–sonde profiles is derived by scaling the standard profiles. The surface

albedo is set to values of open ocean, as the selected cases are performed over open ocean

only. In situ measurements performed after the radiation measurements ruled out the exis-

tence of ice crystals for the investigated cases. Therefore, optical properties of cloud droplets

are assumed and calculated from Mie theory.

Figure 5.19a shows an exemplarily field of retrieved τst (60 s measurement duration) from

a measurement during the VERDI campaign on 14 May 2012 (Case V–01). The image is geo-

referenced with regard to the aircraft nadir direction. The FOV of the SMART–Albedometer

is illustrated by the dark–blue (left boarder), red (nadir), and light–blue (right boarder) lines.

With a flight altitude of 2920m, a cloud–top altitude of 900m and a measurement duration

of 60 s at 30Hz and 80m s−1 flight speed, the covered swath was about 1 337m, the flight

path about 5 000m long. Figure 5.19b illustrates the uncertainties of τst quantified by rel-

ative differences between retrieval assuming a ± 6% measurement uncertainty of I↑λ. For

the bright cloud parts, the retrieval uncertainty rises up to 28.2%. Figure 5.19c illustrates

the corresponding frequency distribution of the retrieved field of τst presented in Fig. 5.19a.

It shows a monomodal distribution with values of retrieved τst ranging from 5 to 16. The

average of τst is 10.6 with a standard deviation of στ =1.6.

In Tab. 5.5 statistical parameters of the ten retrieved fields of τst, including information on

the measurement time, cloud top altitude (hct), field size (swath, length), and average and

standard deviation of τst (τst ± στ ) are provided. The average swath of the covered fields

has a size close to 1.3 km. The length varies from 4 km up to 26 km. Thus, sufficiently large

areas of the clouds are covered to provide a statistically firm analysis of τst and to investigate

horizontal inhomogeneities in the fields of τst (provided in Chapter 6). The average of τst of

all cases ranges between 3 and 14 with most τst between 3 to 7. στ reaches values from 15

to 34% of τst.

5.6. Cloud Optical Thickness Retrieval 73

Figure 5.19: (a) Georeferenced field of τst of Arctic stratus. Cutout from measurement case V-01with 60 s measurement duration. (b) Relative uncertainty of τst field illustrated in (a), retrieved withradiance data varied by ± 6%. The dark–blue, red, and light–blue lines illustrate the FOV of theSMART–Albedometer. (c) Frequency distribution of retrieved τst from (a).

The uncertainty of the simulations applied to the retrieval is estimated equally to the method

presented in Eq. (4.1). It is defined by:

∆τst = 100% ·(τst,BM − τst

τst,BM

)(5.7)

For each simulated τst,BM from the benchmark retrieval, the simulations are repeated. In

the second run, model input parameters are varied by their measurement uncertainty. ∆τst(in %) quantifies the resulting differences compared to the benchmark case. Measurement

uncertainties of the relative humidity and temperature profile are specified by the manufac-

turer Vaisala: ± 2% for relative humidity and ± 0.2C for temperature. The surface albedo

is varied by 10%. According to the specifications of the Sun photometer, the aerosol optical

thickness is varied by ± 0.05. A further source of error is the uncertainty of the retrieved reff,

provided by the SMART–Albedometer. Bierwirth et al. (2013) estimated an uncertainty of

9.5% in the retrieved reff. For the uncertainty of the AisaEAGLE radiance measurements,

a 6% measurement error (related to the radiometric calibration) is assumed. The contri-

bution of all error sources are summarized in Tab. 5.6. A comparison to the calibration


Table 5.5: Measurement period, cloud top altitude, swath, length, and average and standard de-viation (τst ± στ ) of the retrieved fields of τst from suitable VERDI cases (V-01–V-10). The flightaltitude is at 2920m for each case.

Case Day Time (UTC) hct(m) Swath (m) Length (m) τst ± στV-01 14 May 2012 20:31:47-20:36:31 900 1 337 21 277 9.93± 1.89V-02 14 May 2012 20:38:04-20:42:09 850 1 368 20 825 7.82± 2.01V-03 14 May 2012 20:53:26-20:58:30 850 1 368 26 848 3.82± 1.33

V-04 15 May 2012 18:41:53-18:43:58 1 000 1 273 10 503 14.34± 2.54V-05 15 May 2012 21:05:10-21:09:24 930 1 317 20 215 6.35± 0.97

V-06 16 May 2012 19:10:56-19:15:56 1 000 1 273 23 103 6.52± 1.48

V-07 17 May 2012 16:53:23-16:56:06 250 1 750 12 743 3.04± 0.66V-08 17 May 2012 17:00:59-17:06:15 1 000 1 273 25 653 5.48± 1.84V-09 17 May 2012 17:09:28-17:10:38 2 250 477 5 463 7.07± 1.41V-10 17 May 2012 18:49:26-18:50:16 230 1 763 4 103 4.15± 0.67

Table 5.6: Forward model errors ∆τst (in %) for different error sources: effective radius, surfacealbedo, aerosol optical thickness, temperature T , relative humidity RH.

Error Source Variation ∆τst (%)

Effective Radius reff ± 9.5% 0.3–0.5Surface Albedo αsurf ± 10% 0.1–0.6Aerosol Optical Thickness τaer ± 0.05 0.6–0.9Temperature T ± 0.2K 0.0–0.1Relative Humidity RH ± 2% 0.0–0.1

uncertainty of 6% shows that the calculated values of ∆τst are dominated by the measure-

ment uncertainty of the AisaEAGLE radiance (compare Fig. 5.19b). All other error sources

are below 1%.

75

6 Directional Structure of Cloud

Inhomogeneities

Retrieved fields of τ presented in Chapters 4 and 5 are analyzed to quantify horizontal

inhomogeneities of two different cloud types; cirrus and Arctic stratus. Such investigations

are suitable to obtain necessary information (e.g. degree of inhomogeneity, inhomogeneity

distributions), which for example are needed as an input for cloud-resolving models or to

generate surrogate clouds. The latter are synthetic 2D or 3D cloud fields, which share several

important statistical properties with real measured cloud fields, even though they can be

simplified in a way, which changes their appearance significantly from that of real cloud

fields (Venema et al., 2006). The statistic evaluation of the horizontal inhomogeneity of the

fields of τ from the CARRIBA and VERDI campaigns uses 1D inhomogeneity parameters

from the literature (Sect. 6.1), 2D auto–correlation functions (Sect. 6.2) and 2D Fourier

analysis (Sect. 6.3).

6.1 Analysis with 1D Inhomogeneity Parameters

The standard deviation στ of the τ fields for the four CARRIBA and ten VERDI measure-

ment cases has been discussed in Sects. 4.5 and 5.6. However, στ does not allow a comparison

between different cases with different average cloud optical thickness τ . A cloud with higher

τ naturally can exhibit a higher standard deviation. Therefore, Davis et al. (1999) and

Szczap et al. (2000) used a normalized inhomogeneity measure, the relative variability ρτ to

quantify horizontal inhomogeneity of τ in clouds. It is described by the ratio of στ and the

average value of the corresponding sample:

ρτ =σττ. (6.1)

However, the fact that ρτ can exceed values of unity and is a function of the average value

might lead to misinterpretations. Therefore, Davis et al. (1999) and Szczap et al. (2000)

related the relative variability ρτ with the inhomogeneity parameter Sτ in the form:

Sτ =

√ln(ρ2τ + 1)

ln10. (6.2)

In case of a log-normal frequency distribution of τ (base of logarithm is 10), Sτ has a one-

to-one relation to ρτ . The reflected/transmitted radiance is approximately linear to logτ for

moderate τ (for logτ =0.5-1.5 with τ ≈ 3-30). Without net horizontal radiative transport,

76 6. Directional Structure of Cloud Inhomogeneities

where IPA works perfectly, moments of reflected/transmitted radiance are closely associated

with moments of logτ rather than moments of τ (Iwabuchi and Hayasaka, 2002). Thus,

because of its variation between plane-parallel and effective thickness approximations of τ ,

Sτ quantifies the degree of cloud inhomogeneity.

Oreopoulos and Cahalan (2005) investigated the inhomogeneity parameter χτ , first intro-

duced by Cahalan (1994). χτ is defined by the ratio of the logarithmic and linear average of

a distribution of τ :

χτ :=exp(lnτ)

τ, (6.3)

χτ ranges between 0 and 1, with values close to 1 indicating horizontal homogene-

ity, and values close to 0 characterizing a cloud with high horizontal inhomogeneity.

Oreopoulos and Cahalan (2005) state that the reflected solar flux is approximately a lin-

ear function of the logarithm of τ for a wide range (≈ 3 to ≈ 30, depending on θ0) of τ .

Thus, the logarithmically averaged τ provides a way to account for cloud inhomogeneity

effects in plan-parallel radiative transfer calculations by including the nonlinear nature of

the relation between τ and cloud albedo.

The three 1D inhomogeneity parameters ρτ , Sτ , and χτ are calculated for each retrieved field

of τci and τst from the CARRIBA and VERDI campaigns. The results are listed in Tab. 6.1.

Table 6.1: Average and standard deviation (τ ± στ ) and inhomogeneity parameters (ρτ , Sτ , χτ )calculated for retrieved fields of τ from CARRIBA (C-01–C-04) and VERDI (V-01–V-10).

Parameter C-01 C-02 C-03 C-04

ρτ 0.40 0.35 0.17 0.91Sτ 0.19 0.15 0.08 0.48χτ 0.92 0.94 0.99 0.63

Parameter V-01 V-02 V-03 V-04 V-05 V-06 V-07 V-08 V-09 V-10

ρτ 0.19 0.26 0.34 0.18 0.15 0.23 0.22 0.34 0.20 0.16Sτ 0.08 0.11 0.20 0.08 0.07 0.11 0.11 0.15 0.09 0.08χτ 0.98 0.97 0.92 0.98 0.99 0.97 0.97 0.95 0.98 0.99

The cirrus cases show ρτ in the range of 0.17–0.91, Sτ is in the range of 0.08–0.48. The

largest values of ρτ and Sτ are found for 23 April 2011 (C-04), the lowest for 18 April 2011

(C-03). The values for ρτ and Sτ confirm the statement from Sect. 4.5 that the cirrus on

16 and 18 April 2011 was rather homogeneous and the cirrus on 9 and 23 April was rather

inhomogeneous. For the ten Arctic stratus cases, ρτ and Sτ are in the range of 0.15–0.34

and 0.07–0.20, respectively. For stratocumulus Zuidema and Evans (1998) quantified the

inhomogeneity of τ with Sτ =0.1–0.3. Iwabuchi (2000) and Iwabuchi and Hayasaka (2002)

investigated the inhomogeneity of τ for overcast boundary layer clouds and found values

of Sτ =0.03–0.3, which lead to ρτ =0.07–0.78. Thus, the derived values from CARRIBA

and VERDI compare well with the values reported by Zuidema and Evans (1998), Iwabuchi

6.2. Spatial 2D Auto-Correlation and De-Correlation Length 77

(2000), and Iwabuchi and Hayasaka (2002). Out of all ten cases, ρτ and Sτ indicate case

V–03 and V–08 to be more inhomogeneous than the other ones.

For CARRIBA, the values of χτ range from 0.63 to 0.99, indicating a rather inhomogeneous

cirrus on 23 April 2011 (C-04) and rather homogeneous cirrus during the other days. In

contrast to the results for ρτ and Sτ , χτ indicates the cirrus on 9 April 2011 as less in-

homogeneous. The calculated values of χτ for the retrieved fields of τst from the VERDI

campaign gives χτ > 0.9 in each case, with lowest values for case V-03 and V-08, which

already were indicated by ρτ and Sτ to be more inhomogeneous than the other cases. De-

pending on cloud type, cloud phase, hemisphere, surface type, season, and time of day,

Oreopoulos and Cahalan (2005) estimate the range of χτ from ≈ 0.65 to 0.8.

The comparison to the literature values and to the results obtained in Chapters 4 and 5 shows

that the derived 1D inhomogeneity parameters ρτ , Sτ , and χτ are suitable to characterize the

general character of clouds with regard to their inhomogeneities. They are easy to calculate

and are suitable to improve the results of simulations, which assume horizontal homogeneous

clouds. However, ρτ , Sτ , and χτ do not provide a measure of the directional variability of

the inhomogeneities, but different cloud types exhibit horizontal inhomogeneities of different

size and orientation. For example, the observed clouds from the CARRIBA and VERDI

campaigns are different in most aspects (e.g. cloud altitude, cloud structure, cloud phase,

particle size and shape), but ρτ , Sτ , and χτ yield comparable values. Therefore, in order

to characterize cloud inhomogeneities of different cloud types as an input for e.g. cloud-

resolving models or to generate surrogate clouds it is necessary to investigate not only the

mean horizontal inhomogeneity but also its directional dependence (Hill et al., 2012).

6.2 Spatial 2D Auto-Correlation and De-Correlation Length

To quantify the directional inhomogeneities in the retrieved fields of τ , spatial 2D auto–

correlation functions are calculated. The resulting auto–correlation coefficients Pτ describe

the correlation of a τ field with itself, when it is spatially shifted against itself. Thus, spatial

auto–correlation functions measure the degree of similarity between spatially distributed

neighbouring samples. By nature, τ in close collocation show similar values, while cloud pixel

at larger distances can significantly depend on the inhomogeneity of the sampled clouds.

The auto–correlation function Pτ (Lxy) is calculated at fixed distances (lags) Lxy, which

are derived as integer multiples of the equidistant measurement intervals xi and yj(Marshak et al., 1998). Here, with n and m equidistant measurement intervals xi and yj,

Pτ (Lxy) for 2D fields is calculated by:

Pτ (Lxy) = Pτ (−Lxy) =

n,m∑i,j+1

[τ(xi + Lx, yj + Ly)− τ ] · [τ(xi, yj)− τ ]

n,m∑i,j+1

[τ(xi, yj)− τ ]2, (6.4)

τ(xi, yj) is the cloud optical thickness observed at the reference position and τ(xi+Lx, yj+Ly)

the cloud optical thickness at lag Lxy. Pτ (Lxy) yields values between -1 and 1, 1 representing


a perfect positive correlation; a value of -1 is a perfect negative correlation and 0 indicates

no correlation. The largest similarity between both samples is given for a spatial shift equal

to zero (trivial solution). Here, Pτ (Lxy) yields 1. To avoid ambiguous results with respect

to positive and negative correlations, the squared auto-correlation function P 2τ (Lxy) is used,

because it only yields values between 0 (no correlation) and 1 (perfect correlation).

Figures 6.1b and 6.1e show examples of P 2τ (Lxy), calculated for selected areas (500 by 500

Pixels, Fig.6.1a and b) of the fields of τsi from case C-01 (in Fig.4.10a from 3.8 to 7.3 km

along swath and from 0.0 to 3.5 km across swath) and C-03 (in Fig.4.10c from 5.0 to 8.5 km

along swath and from 26.5 to 30.0 km across swath) with Lxy = 250. The magnitude of

P 2τ (Lxy) ranges from 0 to 1 and is illustrated by the color coding. Based on the term

Pτ (Lxy) = Pτ (−Lxy) in Eq. (6.4), the fields of P 2τ (Lxy) are symmetrically with respect to

the center of the images at Lxy = 0. Both cases show a different pattern of the decrease

of P 2τ (Lxy) with increasing absolute value of Lxy. The magnitude of decrease depends on

the horizontal structure of the cloud inhomogeneities. The P 2τ (Lxy) calculated from C-01

(Fig. 6.1b) show a regular shaped decrease, independent on the direction. In contrast, the

P 2τ (Lxy) calculated from C-03 (Fig. 6.1e) show a directional dependence.

Figure 6.1: (a) Selected cloud scene (3.5 by 3.5 km) of field of τci from case C-01. (b) Color coded2D field of P 2

τ (Lxy), calculated for field of τci from (a). Blue and red line illustrate the lags, selectedfor the illustration in (c). White line illustrates ξτ at P 2

τ (Lxy)= 1/e. (c) Average P 2τ (Lxy) (solid

lines) and derived ξτ (dotted lines) along Lx (blue) and Ly (red) from (b). (d) Same as (a) for caseC-03. (e) Same as (b) for selected τci field shown in (c). (f) Same as (c) for P 2

τ (Lxy) shown in (b).

6.2. Spatial 2D Auto-Correlation and De-Correlation Length 79

The squared spatial auto–correlation function P 2τ (Lxy) are used to calculate the de–

correlation length ξτ with:

P 2τ (ξτ ) = 1/e. (6.5)

The de-correlation length quantifies the lag Lxy, at which P 2τ (Lxy) is decreased to a given

value, usually 1/e:

ξτ = Lxy(P2τ = 1/e). (6.6)

ξτ quantifies a length scale where individual cloud parcels are de-correlated and provides

the size of typical cloud inhomogeneities; an increase in inhomogeneities yields a decrease in

ξτ . In Fig. 6.1b, ξτ (at P 2τ (Lxy)= 1/e, indicated by white line) along lag Lx is similar to ξτ

along lag Ly. In Fig. 6.1e, ξτ along lag Lx is significantly smaller than ξτ along lag Ly. This

directional dependence is related to the structure of the cloud with regular filaments in the

swath direction of the image in Fig. 6.1d. For case C-01 the symmetric 2D auto-correlation

functions allows to use a single de-correlation length independent of direction to characterize

the cloud inhomogeneities. For regularly structured clouds such as C-03, however, the 2D de-

correlation can be split into a component of the largest variability and a component along the

smallest variability of τ . In the example both major axis align with the x and y direction.

To estimate the magnitude of the uncertainties and to give quantitative values of ξτ for

the retrieved fields of τ from the CARRIBA and VERDI campaigns, 1D auto–correlation

functions are applied along lag Lx (↔, blue) and along lag Ly (, red) separately.

Figures 6.1c and 6.1f show the corresponding 1D P 2τ (Lxy) as a function of Lxy. For case

C-01 (Fig. 6.1a to c), the derived 1D P 2τ (Lxy) are almost similar and ξ

τ = 634m compares

well with ξ↔τ = 477m within the range of standard deviation given in Tab. 6.2. For case

C-03 (Fig. 6.1d to f), the 1D P 2τ (Lxy) differ significantly from each other and ξ

τ = 3154m

is about seven times larger than ξ↔τ = 434m. Thus, for clouds with a prevailing directional

structure it is advisable to give variable ξτ as a function of observation direction, e.g., by

two parameters, ξτ along and ξ↔τ across the prevailing cloud structure.

The resulting ξ↔τ and ξτ of all measurement cases from CARRIBA and VERDI are sum-

marized in Tab. 6.2. Additionally, ξτ ± σξ are included (ξτ ± σξ,ξ

↔τ ± σξ). Those values

illustrate the pixel by pixel variability for all calculated P 2τ (Lxy) along one direction. Due to

the exponential behavior of P 2τ (Lxy) they are asymmetric with respect to ξ

τ and ξ↔τ .

For CARRIBA, ξτ varies in a range from 434 to 3 154m, depending on the cloud structure

and inhomogeneity. The rather inhomogeneous cases C-01 and C-04 with highly variable τcion small scales yield rapidly decreasing P 2

τ (Lxy) with low ξτ . In contrast, the rather homo-

geneous cases C-02 and C-03 yield slowly decreasing P 2τ (Lxy) and larger ξτ . The differences

between ξτ and ξτ

↔reach up to 85%.

For the Arctic stratus fields observed during VERDI, ξτ and ξ↔τ range between 35m and

278m and are significantly smaller (more inhomogeneous) than those from CARRIBA, al-

though the inhomogeneity parameters from Tab. 6.1 yield similar values. This illustrates

that the inhomogeneity parameters ρτ , Sτ , and χτ are not well suited to compare different

types of clouds. A comparison can only indicate differences with regard to the evaluation of


Table 6.2: De–correlation length calculated for the retrieved fields of τ from CARRIBA (C-01 toC-04) and VERDI (V-01 to V-10). Vertical arrows () indicate the calculation of P 2

τ (Lxy) andsubsequent derivation of ξτ along Ly, horizontal arrows (↔) along Lx. ξτ is the average of all pixels,ξτ − σξ is the average minus standard deviation, and ξτ + σξ is the average plus standard deviation.

Parameter C-01 C-02 C-03 C-04

ξτ − σξ (km) 0.56 1.41 2.62 0.69

ξτ (km) 0.63 1.53 3.15 0.90

ξτ + σξ (km) 0.75 1.67 3.83 1.24

ξ↔τ − σξ (km) 0.31 0.66 0.26 0.35ξ↔τ (km) 0.48 0.76 0.43 0.48ξ↔τ + σξ(km) 0.88 0.86 0.80 0.76

Parameter V-01 V-02 V-03 V-04 V-05 V-06 V-07 V-08 V-09 V-10

ξτ − σξ (km) 0.16 0.19 0.24 0.08 0.11 0.13 0.16 0.12 0.08 0.09

ξτ (km) 0.19 0.28 0.25 0.09 0.13 0.21 0.24 0.23 0.11 0.15

ξτ + σξ (km) 0.26 0.52 0.27 0.11 0.13 0.37 0.48 0.65 0.15 0.27

ξ↔τ − σξ (km) 0.04 0.07 0.06 0.04 0.03 0.03 0.05 0.06 0.02 0.04ξ↔τ (km) 0.06 0.10 0.10 0.06 0.05 0.05 0.08 0.09 0.04 0.06ξ↔τ + σξ (km) 0.10 0.16 0.17 0.10 0.07 0.08 0.15 0.15 0.06 0.09

the horizontal dependence of cloud inhomogeneities. Comparably to the CARRIBA cases,

the differences between ξτ and ξ↔τ are significant as well. They reach up to 77%.

6.3 Power Spectral Density Analysis

Multiple scattering in complex 3D microphysical cloud structures causes a smoothing of

the reflected Iλ above clouds (Cahalan and Snider, 1989; Marshak et al., 1995). This effect

causes uncertainties in the retrieved fields of τ , when homogeneous plan-parallel clouds are

assumed in the retrieval algorithm. This smoothing effect is analyzed using the Fourier

transform of the retrieved fields of τ . The application of Fourier transforms for the investi-

gation of cloud inhomogeneities is most widely used in the existing literature (e.g., Cahalan,

1994; Davis et al., 1999; Schroeder, 2004). However, in most studies presented in literature,

the 1D Fourier transformation is applied to time series of radiative quantities such as Iλ or

γλ. Here, a 2D Fourier transformation is applied to spatial 2D cloud scenes. However, in

Sect. 4.4 it was shown that features of the scattering phase functions are imprinted in the Iλmeasurements of AisaEAGLE. To avoid artifacts in the Fourier transform arising from those

features, fields of τ are used for the analysis, since they account for such scattering features.

6.3. Power Spectral Density Analysis 81

The Fourier transformation decomposes a periodic function into a sum of sinusoidal base

functions. For a given measurement signal, here τ(x, y), the 2D Fourier transform Fτ (kx, ky)

is defined by:

Fτ (kx, ky) =

∫ ∞

−∞

∫ ∞

−∞τ(x, y)e−2πi(kxx+kyy) dxdy, (6.7)

with:

i =√−1. (6.8)

Each of the base functions is described by a complex exponential of different frequency. The

fields of τ are given as a function of horizontal distances x and y. Therefore, wave numbers

kx = 1/x and ky = 1/y are used in the base functions.

For the calculation, theDiscrete FourierTransform (DFT) is applied. With n andm discrete

elements xi and yj (τ of each pixel along and across swath), the 2D DFT is derived by:

DFT(kx, ky) =1

nm

n−1∑xi=0

m−1∑yj=0

τ(xi, yj) e−2πi(

kxxin

+kyyjm

). (6.9)

Figures 6.2 and 6.3 present the Fourier transform by the power spectral densities E(kx) and

E(ky) (in the following called E(kx,y)), calculated from the complex Fourier coefficients by:

E(kx,y) = DFT2(kx,y) (6.10)

Figures 6.2a to 6.2c show τci fields of three selected clouds (3.5 by 3.5 km) from the cases C-01,

C-02, and C-03. C-01 represents an inhomogeneous cirrus without a preferred direction in the

cloud structure (Fig. 6.2a). In C-02 a homogeneous cirrus with a slight directional structure

(Fig. 6.2b) is selected while in C-03 an inhomogeneous cirrus with a distinct directional

structure (Fig. 6.2c) is selected. Figure 6.2d to f show the corresponding 2D power spectral

densities E(kx,y). Largest E(kx,y) are found at smallest wave numbers kx,y, which are located

in the center of the image. The E(kx,y) decrease with increasing kx,y. Inhomogeneous clouds

(Fig. 6.2d and f) show higher values of E(kx,y) over a wide range of wave numbers kx,y,

whereas the larger E(kx,y) for homogeneous clouds (Fig. 6.2e) are only located close to the

smallest wave numbers kx,y. Furthermore, the decrease of E(kx,y) is rotational symmetrical

for clouds with no preferred directional structure (Fig. 6.2d), but asymmetrical for clouds

with a prevailing directional structure (Fig. 6.2e,f).

To study the symmetry, Fig. 6.2g to f show the E(kx,y) along (black, Ea) and across (red, Eb)

the direction of the longer symmetry axis. For the inhomogeneous case without a prevailing

directional structure (C-01), both components Ea and Ea are almost identical. For the

homogeneous case with a slight directional structure (C-02), both Ea and Eb are similar over

most of the covered range of kx,y, except for the smallest wave number kx,y < 3 km−1. For

the inhomogeneous case with a distinct directional structure (C-03), both Ea and Ea are

similar only at kx,y > 7 km−1. The differences in Ea and Eb for the clouds with a prevailing

directional structure result from the different kx,y, at which the signal turns into white noise


Figure 6.2: AisaEAGLE image (3.5 by 3.5 km), 2D power spectral density E(kx,y), and 1D powerspectral density E(kx,y) along (black arrows, Ea) and across (red arrows, Eb) the prevailing di-rection of scale invariant areas for (a),(d),(g) inhomogeneous cloud without directional structure,(b),(e),(h) homogeneous cloud with slight directional structure, and (c),(f),(i) inhomogeneous cloudwith distinct directional structure. The ξτ,s are marked with colored dashed lines.

(constant E(kx,y), independent on kx,y). This transition is used to characterize the small-

scale break ξτ,s, which determines the lower size range of the detected cloud inhomogeneities

(respectively instruments resolution, if ξτ,s is smaller than the pixel size). To derive ξτ,s,

fits are applied to the two scale-invariant regimes of E(kx,y) (exemplary shown for Eb in

Fig. 6.2i). Subsequently, the small scale break ξτ,s is determined by the intersection of those

fits. The corresponding kx,y give ξτ,s. ξτ,s(Ea) and ξτ,s(Eb) for case C-01 are at about 0.03 km.

ξτ,s(Ea) and ξτ,s(Eb) of Case C-02 are at about 0.09 and 0.03 km, respectively. ξτ,s(Ea) from

case C-03 is at about 0.03 km, while ξτ,s(Eb) is at about 0.01 km, which is already close to the

pixel size. Thus, ξτ,s yields quantitatively larger values along the prevailing cloud structure

than across the prevailing structure.

6.3. Power Spectral Density Analysis 83

Marshak et al. (1995) discussed that cloud inhomogeneity and horizontal photon transport

are scale–dependent processes. The E(kx,y) of cloud optical and microphysical are propor-

tional to kβx,y. At large scales, the E(kx,y) of e.g. Iλ, τ , LWC, or IWC follow Kolmogorov’s

β = −5/3 law of energy distribution in a turbulent fluid (Kolmogorov, 1941). For ho-

mogeneous clouds without horizontal photon transport, E(kx,y) follows β = −5/3 for all

kx,y. In that case the variability in the radiation field follows the variability in LWC. In-

creasing cloud inhomogeneity causes a decrease of β of optical properties for smaller scales

(typically < 1000m), but not in β of microphysical properties. Due to horizontal photon

transport the slope of the optical quantities (Iλ, τ) differs from the slope of the microphysical

properties (LWC, IWC). In the following, the horizontal scale, at which the power spectra

starts to deviate from the -5/3 law defines the large-scale break ξτ,L. ξτ,L depends on the

size of the horizontal cloud structures; more inhomogeneous clouds with larger variability on

smaller scales yield smaller ξτ,L. For scales smaller than ξτ,L, the radiative smoothing leads

to uncertainties in 1D cloud retrievals, which not account for the horizontal photon transport

Cahalan (1994); Marshak et al. (1998); Zinner et al. (2006); Varnai and Marshak (2007).

A comparison of the depicted E(kx,y) to the -5/3 law in Fig. 6.2g to h shows that the

selected cirrus cases do not contain the larger scales, which are necessary to identify ξτ,L.

The depicted E(kx,y) belong to kx,y lower than ξτ,L, which already exhibit a steeper slope

than β = −5/3. Therefore, the size of the selected areas is suitable to identify quantitative

values for ξτ,s, but for deriving ξτ,L, larger fields of τ have to be considered. Unfortunately,

this is only possible for calculations of the DFT along Ly (across swath). Calculations along

Lx (swath) do not cover a sufficiently large distance to derive quantitative values for ξτ,L.

Therefore, the following analysis is performed using 1D DFT along Ly only. To evaluate

the resulting 1D Fourier spectra with reduced noise (rn) characteristics, the Ern(k) ∼ kβ

are calculated with the use of octave binning, following the method proposed by Davis et al.

(1996), Harris et al. (1997), and Schroeder (2004). Here, for the total number N of E(ky)

the binning of ky is specified by factors of 2n with n=0,1,...,log2(N -2). Using those factors,

bins for the wave numbers are generated and the corresponding E(ky) within the particular

bin size averaged. In addition to the reduced noise of E(krn) compared to E(ky) the binning

provides a uniformly contribution of all scales to the average values.

Figure 6.3a and b show the 1D DFT calculated across the swath for two typical cases of

cirrus (CARRIBA case C-01) and Arctic stratus (VERDI case V-07). The two cases are

selected, since they exhibit a similar length Ly. For each line of the τ field (each swath

pixel) E(ky) is calculated and the individual power spectra are overlayed as gray dots in

Fig.6.3. The E(krn) derived from the octave binning are included as black squares. They

provide the supporting points for the slope fits. A green line indicates the β = −5/3 law.

For large scales, the Ern(ky) (blue fit) approximately follow the −5/3 relation in both cases.

The large-scale break (ξτ,L) is evident at the intersection between the blue and the red line.

Here, the slope in the Ern(ky) becomes steeper. For the CARRIBA case ξτ,L yields 0.31 km

and the middle scale slope βm decreases to -2.2. ξτ,L for the VERDI case yields 0.06 km and

βm decreases to 2.2. The middle–scale slope βm is a function of the inhomogeneity in the

measured signals. With increasing inhomogeneity of the optical thickness τ , βm decreases.

Together with the smaller ξτ,L, this indicates that the stratus cloud of the VERDI case is


more inhomogeneous compared to the cirrus cloud. As discussed above, ξτ,s is observed at

the intersection between the fits for the middle (red, βm) and small scales (orange, βs). Due

to the analysis of a significant larger distance compared to Fig. 6.2, it is highly uncertain to

give quantitative numbers for ξτ,s. Therefore, it is indicated only qualitatively.

Figure 6.3: 1D power spectral density E(ky) (gray dots) for each spatial pixel on the swath axis ofthe τ field from (a) case C-01 and (b) case V-07. Scale-invariant slopes β are marked with coloredsolid lines. The E(krn) derived from the octave binning are included as black squares. Scale breaksξτ,L and ξτ,s are indicated by dashed lines.

Table 6.3 summarizes the ξτ,L for all available cloud cases from CARRIBA and VERDI. The

values compare well with the de-correlation length ξτ derived in Sect. 6.2. Although the exact

values of ξτ,L are not equal to ξτ , both are in the same size range for each individual case.

Similar to ξτ given in Tab. 6.2, ξτ,L indicates that C-02 and C-03 are more homogeneous

than C-01 and C-04. In general it was found that the cirrus observed during CARRIBA are

more homogeneous than the Arctic stratus from VERDI.

Table 6.3: Scale breaks ξτ,L calculated along Ly for the retrieved fields of τ from CARRIBA (C-01to C-04) and VERDI (V-01 to V-10).

C-01 C-02 C-03 C-04

ξτ,L (km) 0.31 1.30 2.83 0.20

V-01 V-02 V-03 V-04 V-05 V-06 V-07 V-08 V-09 V-10

ξτ,L (km) 0.16 0.11 0.19 0.17 0.12 0.10 0.06 0.12 0.19 0.13

85

7 Summary and Conclusions

During the two international field campaigns CARRIBA and VERDI, downward and up-

ward solar spectral radiance (I↓λ, I↑λ) were measured with high spatial resolution (< 10m),

using the imaging spectrometer AisaEAGLE. The instrument was carefully characterized and

calibrated in the laboratory and the procedure of data evaluation (dark current correction,

calibrations, smear correction) was described. It was shown that the dark current and smear

correction should always be taken into account (calibration included). Furthermore, based

on the given measurement geometry the scattering angle ϑ of the incident Iλ were calculated

and allocated to each spatial pixel.

The measured fields of I↓λ and I↑λ from CARRIBA and VERDI were used to retrieve fields

of τ with high spatial resolution (< 10m). To derive the fields of τ , different methods for

CARRIBA and VERDI were derived and applied. For the cirrus observed during CARRIBA,

the most probable crystal shape was derived. For the Arctic stratus observed during VERDI,

the sea-ice albedo complicated the retrievals of τst. The influence of the highly reflecting sea

ice as well as large albedo contrasts on the retrieval of τst were investigated.

The derived fields of τ from CARRIBA and VERDI were used to quantify horizontal cloud

inhomogeneities. Parts of this chapter were already published in Schafer et al. (2013) and

Schafer et al. (2015).

7.1 Subtropical Cirrus Optical Thickness Retrieval from

Ground–Based Observations

The cirrus optical thickness τci was retrieved from ground–based AisaEAGLE I↓λ measure-

ments. Based on four cases collected during CARRIBA on Barbados in 2011, the feasibility

of retrieving τci at high spatial resolution was demonstrated. A preliminary characterization

of the cirrus inhomogeneity using the average and standard deviation, as well as frequency

distributions was performed. The cirrus observed on 16 and 18 April 2011 was quite homoge-

neous with mean τci of 0.28 and 0.20 and coefficients of variation of 0.09 and 0.03. On 9 and

23 April 2011 rather inhomogeneous cirrus with mean τci of 0.41 and 0.05 and coefficients of

variation of 0.17 and 0.04 was observed.

The sensitivity of the retrieval method with respect to surface albedo, effective radius, cloud

altitude, and ice-crystal shape was characterized by varying the model input parameters.

Largest sensitivities of the retrieved τci have been found with respect to the surface albedo

and the ice-crystal shape with up to 30% and 90% differences. The sensitivities of the

86 7. Summary and Conclusions

retrieved τci with respect to effective radius (≤ 5%) and cloud altitude (≤ 0.5%) are com-

parably small. This indicates that accurate knowledge of the surface albedo and ice-crystal

shape is required to reliably retrieve cirrus optical thickness with AisaEAGLE. However, the

determination of the ice-crystal shape is complicated without in situ measurements inside

the cirrus. AisaEAGLE measures radiance as a function of a wide range of scattering angles.

Therefore, it provides information about the scattering phase function. An evaluation of ice

crystal shape is obtained by comparing the radiance measured by AisaEAGLE to simulations

and all-sky images. It is possible to distinguish between hexagonal ice crystals that produce

the typical 22 halo and irregular ice crystals that do not. The shape retrieval is limited to

a narrow range of scattering angles, which does not always cover the halo.

Therefore, the optimum way to operate AisaEAGLE in a ground-based application with

a large coverage of scattering angles is to adjust the sensor line along the azimuthal direction

of the Sun. In this way, the maximum possible range of the scattering phase function is

detected. However, due to a variable wind direction the clouds may not head perpendicular

across the sensor line, which causes then a spatial distortion of the cloud shape. For slow

moving cirrus and the assumption that the crystal shape stays constant over the time period

of measurements, two measurements can be combined; using at first an orientation of the

sensor line along the azimuthal direction of the Sun to detect the scattering phase function

and varying afterwards the orientation of the sensor line perpendicular to the heading of the

cirrus. For fast moving cirrus, a compromise has to be made between the maximum possible

range of detectable scattering angles or measurements without spatial distortion of the cloud

field.

7.2 Arctic Stratus Cloud Retrieval from Airborne Observations

During VERDI, carried out in Inuvik, Canada in 2012, the AisaEAGLE measurements

of I↑λ were performed from an aircraft. In combination with the nadir pointing SMART-

Albedometer, the reflectivity γλ was derived. Measurements above clouds in situations with

heterogeneous surface albedo were analyzed in order to retrieve τst. Due to the high contrast

in the surface albedo of sea ice and open water, the data showed a distinct difference between

γλ above water and sea-ice surfaces. This transition was used to establish a sea–ice mask.

Threshold values for γλ derived from both measurements and radiative transfer simulations

are in good agreement.

In the vicinity of ice edges, γλ is reduced/enhanced above the bright sea ice/dark ocean

surface. This is related to 3D effects, which result from isotropic reflection on the bright

sea ice, which causes horizontal photon transport, before the radiation is scattered by cloud

particles into the direction of observation. To quantify the uncertainties of the cloud retrieval

in such areas of open water close to ice floes, γλ measurements from the VERDI campaign

were analyzed using 3D radiative transfer simulations for a cloudless case and clouds of

τst = 1/5/10 located above various, idealized surface albedo fields. Two distances ∆LHPT

and ∆L were defined to characterize the extent of the horizontal photon transport (∆LHPT)

and to estimate the distance to the ice edge (∆L) within which the retrieval of τst and reff is

biased stronger by the 3D effects than by measurement uncertainties.

7.2. Arctic Stratus Cloud Retrieval from Airborne Observations 87

From the measurement cases (τst = 5, hcloud = 0–200m), a distance ∆L of 400m was

derived. Radiative transfer simulations, adapted to the observed cloud and sea-ice situation,

confirmed this value. For the case of the infinitely straight ice edge, a distance ∆LHPT =

100m/250m/300m was found for τst = 1/5/10. The increase of ∆LHPT shows that the

horizontal photon transport is increasing with increasing τst. However, the minimum distance

∆L to the ice edge, where a 1D cloud retrieval can be applied, is decreasing with increasing

τst (∆L = 600m/400m/250m at τst = 1/5/10) due to the stronger impact of measurement

uncertainties in the case of thicker clouds (higher γλ).

The simulations did not show significant differences of ∆LHPT and ∆L assuming various reffbetween 10–30 µm. Besides cloud properties, the influence of the magnitude of the albedo

contrast was tested. Varying the simulated surface albedo of the bright sea ice and dark

ocean water by ±6%, ∆LHPT and ∆L were found to vary by < 1%, which is less than the

measurement uncertainty of 6%. This indicates that ∆LHPT and ∆L are robust measures

to quantify the horizontal extent of the 3D radiative effect at various albedo contrasts.

The cloud altitude and cloud geometrical thickness significantly influence ∆L. The distance

∆L increases linearly with increasing cloud base altitude (for τst = 5 from 800 to 3200m for

a 500m thick cloud with cloud base at 0 and 1500m). The same increase of ∆L holds for an

increasing cloud geometrical thickness (for τst = 5 from 300 to 2000m for a 200 and 1500m

thick cloud). Therefore, the cloud base altitude and geometrical thickness have to be known

while performing 3D radiative transfer simulations of clouds above ice edges.

To investigate changes in the 3D radiative effect due to variations in the ice-edge length or sea-

ice area, area-averaged γλ were calculated for different idealized cases of sea-ice distributions.

A larger enhancement of the area-averaged γλ was found for longer ice-edge lengths. Changes

in the sea-ice area are of less importance. Placing the ice floes directly next to each other,

an enhancement of the area-averaged γλ was found as well, although the sea-ice area and

ice-edge length remained the same.

For the direct comparison of simulation and measurement, an observed ice-floe field was

modeled. The frequency distributions of observations and simulations agree within the mea-

surement uncertainties. The area-averaged γλ showed stronger 3D effects for the real case

compared to the idealized cases simulated before. A quantification of the 3D radiative effect

in clouds above ice edges is only simulated if realistic surface albedo fields are applied. How-

ever, a parameterization of the influence of individual parameters is only possible by using

such simplified surface albedo fields.

The results from the simulations suggest that applying a 1D cloud retrieval to airborne

measurements taken over ocean areas located close to sea ice edges will result in an over-

estimation of τst and reff and the overestimation will increase with proximity to the ice edge.

This overestimation was calculated for a liquid water cloud with τst = 10.0 and reff=15 µm.

In that case, the overestimation of the retrieved τst reaches up to a distance of 1.5 km from

the ice edge, with a maximum overestimation of 90% directly beside the ice edge. For reff,

an overestimation of 30% was found in the direct vicinity of the ice edge. 3D influences

on the retrieval of reff are observable up to a distance of 1 km from the ice edge. This is


slightly lower compared to the distance where τst is biased, which indicates that the 3D effect

depends on wavelength.

An important implication from Chapter 5 is that only γλ measurements far away from any

ice edge were used for a subsequent retrieval of τst. Thus, with the help of the distance ∆L,

ten sections of AisaEAGLE radiance measurements with average swath of 1.3 km and lengths

of 4 to 26 km were identified, which were not biased by a highly reflecting sea-ice albedo or

by large albedo contrasts. The average of τst of all cases gave values of 3 < τst < 14 with

most τst between 3 to 7 and στ in the range of 15 to 34% of τst. A sensitivity study applied

to the retrieval method of τst gave uncertainties in the range of 6.2 to 6.5%, mostly related

to the uncertainty in the radiometric calibration. Thus, sufficiently large areas of the clouds

were covered to provide good statistics on the evaluation of τst with regard to the evaluation

of cloud inhomogeneities.

7.3 Cloud Inhomogeneity Analysis

The investigation of cloud inhomogeneity was performed for the retrieved τ from four cirrus

cases collected during CARRIBA and from ten Arctic stratus cases collected during VERDI.

The cloud inhomogeneity was analyzed by three common 1D inhomogeneity parameters ρτ ,

Sτ , and χτ , with auto–correlation functions, and Fourier analysis.

The results from the calculated 1D inhomogeneity parameters ρτ and Sτ are in agreement

with values given in the literature for similar cloud types. The calculated ρτ are in the range

of 0.17–0.91 for CARRIBA and 0.15–0.34 for VERDI. The literature values are in the range of

0.07–0.78 (except C-04, ρτ =0.91). The inhomogeneity parameter Sτ exhibits values of 0.08

to 0.48 for CARRIBA and 0.07 to 0.20 for VERDI. Literature values are in the range of 0.03

to 0.3. For χτ , the literature estimates values between ≈ 0.65 and 0.8. Here, the difference

to the results from CARRIBA and VERDI is larger. All values except for C-04 (χτ =0.63)

are in the range between 0.92 and 0.99. A further intercomparison between CARRIBA and

VERDI showed that all three inhomogeneity parameters gave values of similar magnitude

for both cloud cases; cirrus and Arctic stratus.

The analysis using auto–correlation functions Pτ (Lxy) showed that an intercomparison of

cirrus inhomogeneities with inhomogeneities in Arctic stratus are not suitable, using the 1D

inhomogeneity parameters ρτ , Sτ , and χτ . For both cloud cases the 1D inhomogeneity pa-

rameters gave similar values, but significant differences resulting from the analysis of Pτ (Lxy),

which additionally contain information on the horizontal structure of cloud inhomogeneities.

Therefore, to compare the inhomogeneities of different cloud types, their horizontal struc-

ture has to be taken into account. From the squared auto–correlation functions P 2τ (Lxy)

the de–correlation length ξτ was derived, which is a measure of the size range of the cloud

inhomogeneities. The 2D analysis of P 2τ (Lxy) revealed that ξτ is a function of the directional

structure of the cloud inhomogeneities. Without knowledge about the directional structure

of cloud inhomogeneities, no universally valid value for ξτ can be derived from the retrieved

fields of τ . The differences in ξτ as derived from a 1D auto–correlation analysis along and

7.4. Perspectives 89

across the prevailing structure of cloud inhomogeneities reached up to 85 and 77% for CAR-

RIBA and VERDI. Thus, the directional cloud structure has to be taken into account for

a quantification of cloud inhomogeneities. The absolute values of ξτ were in the range of 0.43

to 3.15 km for CARRIBA and 0.04 to 0.28 km for VERDI.

Due to a complex 3D microphysical cloud structure, multiple scattering causes a smoothing

of the reflected Iλ field of the cloud. This generates a smoothing effect of the retrieved

fields of τ , which is evident from scale analysis. This effect was quantified using 2D Fourier

transformation applied to the retrieved fields of τ . From the resulting power spectral densities

E(kx,y), evidence of 3D radiative effects were found for both cloud types, cirrus and Arctic

stratus. For larger scales, the E(kx,y) followed Kolmogorov’s -5/3 law. Approaching smaller

scales, the slope became steeper indicating radiative smoothing until it turned into white

noise for scales smaller than the lower size of cloud inhomogeneities. From the intersection

of fits of the three slope regimes, the small-scale break ξτ,s (between small- and middle-scale

slopes) and the large-scale break ξτ,L (between middle- and large-scale slopes) were derived.

Similarly to the analysis using auto–correlation functions, ξτ,s depends on the directional

structure of the cloud inhomogeneities. ξτ,s determines the smallest resolved size of cloud

inhomogeneities (0.01 to 0.09 km in the evaluated cases). Due to a too small swath width,

a similar analysis for ξτ,L could not be performed. However, the calculated ξτ,L along the

image are comparable to the results derived from the analysis of Pτ (Lxy). ξτ,L for CARRIBA

was in the range of 0.20 to 2.83 km. For VERDI a range of 0.06 to 0.19 km was covered by

ξτ,L.

In early studies, by e.g. Marshak et al. (1998) or Schroeder (2004), the scale dependence of

cloud radiation measurements was analyzed along one direction (time series) using 1D DFT.

However, the resulting E(k) are only valid for the particular observation direction along the

given path. Due to prevailing wind directions, clouds tend to evolve directional structures.

In such cases, the calculated E(k), β, ξτ,s, and ξτ,L will only be valid for the whole cloud

if the cloud structure exhibits a non-directional character (compare Fig. 6.2d to f). In all

other cases, significant differences are expectable. Therefore, the directional structure of

cloud inhomogeneities has always to be taken into account. Imaging spectrometers such

as AisaEAGLE help to identify and analyze the prevailing directional structure of cloud

inhomogeneities.

7.4 Perspectives

The assessment of the crystal shape is restricted to the narrow FOV (36.7) of the

AisaEAGLE lens. The detected ϑ-range will be increased using a wide-angle lens (58)

and a scanning version of AisaEAGLE, installed on an astrophysical mount. The additional

angular information will allow to develop a cirrus retrieval technique considering the crystal

shape. This will significantly decrease the retrieval uncertainty. Furthermore, a scanning

version of AisaEAGLE will reduce spatial distortions in the images, because the scans are

then not anymore restricted to the heading of the clouds.


Up to now, the spectral range of the collected fields of Iλ was restricted to the visible wave-

length range (400 nm≤λ ≤ 1 000 nm). Therefore, a retrieval of reff could not be performed.

In future studies, this wavelength range will be extended to the near-infrared wavelength re-

gion (1 000 nm≤λ ≤ 2 500 nm) using collocated measurements with the imaging spectrome-

ter AisaHAWK. Those measurements will also cover absorbing wavelengths, which are sensi-

tive to reff. Furthermore, the extended wavelength range will allow to adopt the multispectral

cloud retrieval from Bruckner et al. (2014) to the imaging spectrometer measurements. This

will avoid ambiguities in the simulations.

The cloud retrievals from the VERDI data were restricted to measurements over open ocean

with a sufficiently large distance to the next ice edge. Therefore, only a limited number of

cases was available, for which a retrieval of τst could be applied. In April 2014, the inter-

national measurement campaign RACEPAC (Radiation-Aerosol-Cloud ExPeriment in the

Arctic Circle) was carried out in Inuvik, Canada. Here, similar measurements compared

to VERDI were performed using the AWI aircraft Polar 5 and 6. While Polar 6 performed

in situ measurements inside the clouds, collocated radiation measurements were performed

with Polar 5. Thus, more data are available to investigate inhomogeneities of Arctic stratus.

Furthermore, single-particle imaging probes such as SID-3 (Small Ice Detector) or HALO-

Holo (Holographic single-particle imager, intially designed for High Altitude and LOng

range research aircraft) were installed aboard Polar 6, which allow comparisons to retrieved

crystal shapes. In addition, during the project AC3 (ArctiC Amplification: Climate Rel-

evant Atmospheric and SurfaCe Processes and Feedback Mechanisms), more investigations

with regard to cloud inhomogeneities in Arctic stratus will be performed. A series of air-

borne, ship- and ground-based measurements are planned. Here, the findings from VERDI

and RACEPAC with regard to 3D radiative effects, which are caused by an inhomogeneous

surface albedo, will be further investigated and additionally linked to satellite observations.

So far, the investigations were performed for cirrus and Arctic stratus. Different clouds will

exhibit different structures and magnitudes of inhomogeneities. Extending the investiga-

tions to a wider field of different cloud types will increase insights to effects related to cloud

inhomogeneities. Accordingly, measurements of cloud sides from deep convective cumulus

using airborne visible and near-infrared imaging spectrometers such as AisaEAGLE and

AisaHAWK were recently performed during the international field campaign ACRIDICON-

CHUVA (Aerosol, Cloud, Precipitation, and Radiation Interactions and DynamIcs of

CONvective Cloud Systems - Cloud processes of tHe main precipitation systems in Brazil:

A contribUtion to cloud resolVing modeling and to the GPM (GlobAl Precipitation Mea-

surement)) in Manaus, Brazil in 2014 (Wendisch et al., 2016). Here, due to the convective

character and different phases, larger 3D effects are expected.

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List of Greek Symbols 101

List of Greek Symbols

α rad or Angle between Particular Applied Directions

αλ,surf - Spectral Surface Albedo

β rad or Diffraction Angle

βi rad or Viewing Zenith of Spatial Pixel i

βl - Large-Scale Slope

βm - Middle-Scale Slope

βs - Small-Scale Slope

γλ - Spectral Reflectivity

γλ - Mean Spectral Reflectivity

γλ,ice - Spectral Reflectivity Above Bright Sea Ice

γλ,water - Spectral Reflectivity Above Dark Ocean Water

γλ,thresh - Spectral Reflectivity Threshold

ϑ rad or Scattering Angle

θ rad or Atmospheric Zenith Angle

θ0 rad or Solar Zenith Angle

λ m Wavelength

µ - Zenith Distance

µ0 - Solar Zenith Distance

µ′ - Cosine of Direction of Incident Radiation

ξτ m De–Correlation Length

ξτ,L m Large-Scale Break

ξτ,s m Small-Scale Break

ρi g m−3 Density of Solid Ice

ρλ - Spectral Cloud Albedo

ρτ - Inhomogeneity Parameter

ρw g m−3 Density of Liquid Water

σ variable Standard Deviation

τ - Cloud Optical Thickness

τaer - Aerosol Optical Thickness

τci - Cirrus Optical Thickness

τci - Mean Cirrus Optical Thickness

τci,BM - Cirrus Optical Thickness of Benchmark Retrieval

τst - Optical Thickness of Arctic Stratus

τst - Mean Optical Thickness of Arctic Stratus

τst,BM - Optical Thickness of Arctic Stratus of Benchmark Retrieval

φ rad or Atmospheric Azimuth Angle

102 List of Greek Symbols

φ0 rad or Solar Azimuth Angle

φ′ rad or Azimuth Angle of Incident Radiation

φsen rad or Sensor Azimuth Angle

Φλ J s−1 nm−1 Spectral Radiant Energy Flux

Φabs J s−1 nm−1 Absorbed Radiant Energy Flux

Φext J s−1 nm−1 Extinguished Radiant Energy Flux

Φsca J s−1 nm−1 Scattered Radiant Energy Flux

χτ - Inhomogeneity Parameter

ω - Single–Scattering Albedo

Ω sr Solid Angle


List of Latin Symbols

AD m2 Projected Area of an Ice Crystal

A∆h - Fit Parameter

Ai m2 Ice Floe Area of Scenario i

B∆h m Fit Parameter

bext m−1 Spectral Volumetric Extinction Coefficient

bsca m−1 Spectral Volumetric Scattering Coefficient

C m Fit Parameter

Cabs m2 Absorption Cross Section

Cext m2 Extinction Cross Section

Csca m2 Scattering Cross Section

d2A m2 Infinitesimal Area Element

d2Ω sr Differential Solid Angle

d m Groove Spacing

D m Diameter of Cloud Particle

∆L m Critical Horizontal Distance to the Ice Edge

∆LHPT m Critical Horizontal Distance to the Ice Edge

related to the Horizontal Photon Transport

E(kx,y) - Power Spectral Density

Ern - Power Spectral Density with Reduced Noise Characteristics

Erad J Radiant Energy

f - Function

fc Wm−2 nm−1 sr−1 Absolute Calibration Factors from Integrating Sphere

Fλ Wm−2 nm−1 Spectral Irradiance

Finc Wm−2 nm−1 Incident Irradiance

F ↓λ Wm−2 nm−1 Downward Spectral Irradiance

F ↑λ Wm−2 nm−1 Upward Spectral Irradiance

hcloud m Cloud Base Altitude

Iλ Wm−2 nm−1 sr−1 Spectral Radiance

I↓λ Wm−2 nm−1 sr−1 Downward Spectral Radiance

I↑λ Wm−2 nm−1 sr−1 Upward Spectral Radiance

Idiff Wm−2 nm−1 sr−1 Diffuse Solar Radiance

Idir Wm−2 nm−1 sr−1 Direct Solar Radiance

Jdiff Wm−2 nm−1 sr−1 Diffuse Source Term

Jdir Wm−2 nm−1 sr−1 Direct Source Term

kx,y m−1 Wavenumber

li m Ice Edge Length of Scenario i

104 List of Latin Symbols

lpix m Spatial Pixel Resolution Across Swath Direction

Lx,y - Lag

m - Number of Elements

M - Defraction Order

n - Number of Elements

n - Unit Vector

npix - Spatial Pixel NumberdNdD (D) m−1 Number Size Distribution

p hPa Mean Surface Pressure

Pτ (Lx,y) - Spatial Auto-Correlation Function

reff µm Effective Radius

rfloe m Radius of Ice Floe

R3D/IPA - Ration between 3D and IPA Simulations

Rice - Ration between 3D and IPA Simulations over Sea Ice only

Rtotal - Ration between 3D and IPA Simulations over Total Domain

Rwater - Ration between 3D and IPA Simulations over Water only

s - Direction of Propagation

s m Swath

Sτ - Inhomogeneity Parameter

S0 Wm−2 nm−1 Extraterrestrial Irradiance

Sc Smear-Corretion Factor

Scal ADU Measurement Signal During Calibration

Sdark ADU Measured Dark Raw Signal

Slum ADU Measured Illuminated Raw Signal

Smeas ADU Raw Measurement Signal

spix m Spatial Pixel Resolution Along Swath Direction

t s Time

tint s Integration Time

tread−out s Read-Out Time

v ms−1 Mean Horizontal Wind

vcloud, aircraft ms−1 Velocity of Cloud or Aircraft

VD m3 Volume of an Ice Crystal

x m Distance

xi - Sampling Frequency

yi - Sampling Frequency

zct m Cloud Top Altitude

zsurf m Surface Altitude

F - Fourier Transform

P - Phase Function

−−→CD - Vector of Incident Radiation between Cloud and Detector−→SC - Vector of Incident Radiation between Sun and Cloud


DFT - Discrete Fourier Transform

FOV rad or Field of View

FOVpix rad or Field of View of Single Pixel

FWHM m Full Width at Half Maximum

IWC gm−3 Ice Water Content

LWC gm−3 Liquid Water Content

SNR - Signal to Noise Ratio

RH % Relative Humidity

List of Abbrevations 107

List of Abbrevations

1D One–dimensional

2D Two–dimensional

3D Three–dimensional

AB Airborne

AC3 ArctiC Amplification: Climate Relevant Atmospheric and SurfaCe

Processes, and Feedback Mechanisms

ACRIDICON Aerosol, Cloud, Precipitation, and Radiation Interactions

and DynamIcs of CONvective Cloud Systems

ADU Analog Digital Units

AMALi Airborne Mobile Aerosol LiDAR

AVHRR Advanced Very High Resolution Radiometer

ARL Air Resources Laboratory

AWI Alfred Wegener Institute Helmholtz Centre

for Polar and Marine Research

BCO Barbados Cloud Observatory

CARRIBA Clouds, Aerosol, Radiation, and tuRbulence in the

trade wind regime over BArbados

CASI Compact Airborne Spectrographic Imager

CCD Charge-Coupled Device

CHUVA Cloud processes of tHe main precipitation systems in Brazil:

A contribUtion to cloud resolVing modeling and to the GPM

COS Cloud Overlap Schemes

DFT Discrete Fourier Transformation

DISORT DIScrete Ordinate Radiative Transfer Solver

ECMWF European Centre for Medium-Range Weather Forecasts

FOV Field Of View

FPS Frames Per Second

FWHM Full Width at Half Maximum

GCM General Circulation Model

GPM Global Precipitation Measurement

GPS Global Positioning System

HALO High Altitude and LOng range research aircraft

HDRF Hemispherical-Directional Reflectance Function

HEY Hong, Emde, Yang

HPT Horizontal Photon Transport

HYSPLIT HYbrid Single-Particle Lagrangian Integrated Trajectory

108 List of Abbrevations

INS Inertial Navigation System

IPA Independent Pixel Approximation

IPCC Intergovernmental Panel on Climate Change

IWC Ice Water Content

LES Large-Eddy Simulation

libRadtran library for radiative transfer

LiDAR Light Detection And Ranging

LIM Leipzig Institute for Meteorology

LOWTRAN LOW Resolution TRANsmission Model parametrization

LUT Lookup Tables

LWC Liquid Water Content

MAS MODIS Airborne Simulator

MCARaTS Monte Carlo Atmospheric Radiative Transfer Solver

MISR Multiangle Imaging SpectroRadiometer

MODIS MODerate-Resolution Imaging Spectrometer

NISE Near Real-Time Ice and Snow Extent

NOAA National Oceanic and Atmospheric Administration

OPAC Optical Properties of Aerosols and Clouds

RACEPAC Radiation-Aerosol-Cloud ExPeriment in the Arctic Circle

RGB red, green, blue

RH Relative Humidity

RTE Radiative Transfer Equation

SBDART Santa Barbara DISORT Atmospheric Radiative Transfer

SID Small Ice Detector

SMART Spectral Modular Airborne Radiation measurement sysTem

SNR Signal–To–Noise Ratio

SoRPIC Solar Radiation and Phase discrimination of ArctIc Clouds

specMACS spectrometer of the Munich Aerosol Cloud Scanner

SSFR Solar Spectral Flux Radiometers

UTC Coordinated Universal Time

VERDI VERtical Distribution of Ice in Arctic clouds

List of Figures 109

List of Figures

1.1 Radiance at 645 nm wavelength of a cloud scene, as observed with different

ground-pixel size resolution of 5m (CASI, specMACS, AisaEAGLE), 50m

(SSFR, SMART), 250m (MODIS), and 1 km (AVHRR). . . . . . . . . . . . . 4

2.1 Illustration of the definition of radiances. . . . . . . . . . . . . . . . . . . . . 10

2.2 Scattering phase functions of a cloud droplet distribution and ice crystals. . . 13

3.1 Optical scheme of an imaging spectrometer. . . . . . . . . . . . . . . . . . . . 18

3.2 Characteristic swath and pixel width for AisaEAGLE. . . . . . . . . . . . . . 18

3.3 Scheme of AisaEAGLEs binning procedure. . . . . . . . . . . . . . . . . . . . 20

3.4 Absolute radiometric calibration setup for AisaEAGLE. . . . . . . . . . . . . 22

3.5 Calibration factors from the absolute radiometric calibration of AisaEAGLE. 22

3.6 Calibration factors from the absolute radiometric calibration of AisaEAGLE

as a function of spatial pixel and wavelength. . . . . . . . . . . . . . . . . . . 23

3.7 Dark current of AisaEAGLE as a function of spatial pixel and wavelength. . . 24

3.8 Linearity of AisaEAGLE measurements. . . . . . . . . . . . . . . . . . . . . . 25

3.9 Illustration of the read-out process and the smear effect. . . . . . . . . . . . . 26

3.10 Spectral radiance measured with AisaEAGLE using different wavelength in-

tervals in the calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.11 Illustration of the ground-based AisaEAGLE measurement geometry. . . . . . 28

3.12 Scattering angle range that can be detected from ground-based and airborne

AisaEAGLE measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1 Site of AisaEAGLE radiance measurements during CARRIBA. . . . . . . . . 34

4.2 Cloud masks derived from LiDAR measurements at the BCO. . . . . . . . . . 35

4.3 Simulated radiance as a function of cloud optical thickness. . . . . . . . . . . 36

4.4 All-sky images at beginning of evaluated AisaEAGLE radiance measurements. 37

4.5 Two-dimensional images of evaluated AisaEAGLE radiance measurements. . 38

4.6 Scattering phase functions for different ice crystal shapes and effective radii. . 39

4.7 Time series of downward solar radiance as a function of scattering angles. . . 40

4.8 Measured and simulated I↓λ as a function of scattering angles ϑ for 18 April 2011. 41

4.9 Measured and simulated I↓λ as a function of scattering angles ϑ for 23 April 2011. 42

4.10 Time series of the retrieved τci. . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.11 Normalized frequency distributions of τci. . . . . . . . . . . . . . . . . . . . . 44

4.12 Retrieval results with regard to the sensitivity of the input parameters. . . . . 45

5.1 Flight tracks performed during the VERDI campaign. . . . . . . . . . . . . . 48

5.2 VERDI flight track and true-color MODIS image from 17 May 2012. . . . . . 50

110 List of Figures

5.3 Simulated γλ as a function of τst and surface albedo. . . . . . . . . . . . . . . 51

5.4 Fraction of occurrence of measured γλ. . . . . . . . . . . . . . . . . . . . . . . 52

5.5 Fields of γλ measured with AisaEAGLE and corresponding ice masks. . . . . 53

5.6 Flight altitude, cloud top altitude and profiles of temperature and relative

humidity from flight on 17 May 2012. . . . . . . . . . . . . . . . . . . . . . . 54

5.7 Normalized frequency of occurrence of measured γλ. . . . . . . . . . . . . . . 55

5.8 Averaged γλ measured perpendicular to the ice edges. . . . . . . . . . . . . . 56

5.9 Sketch of the 3D radiative effects between clouds and surface in the vicinity

of ice floes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.10 Simulated mean γλ across an infinitely straight ice edge for clear-sky conditions

as well as for low-level clouds of different τst. . . . . . . . . . . . . . . . . . . 59

5.11 Simulated γλ as a function of τst and cloud geometry. . . . . . . . . . . . . . 60

5.12 Distance ∆L as a function of τst and cloud geometry. . . . . . . . . . . . . . . 61

5.13 Simulations and parameterizations of ∆L as a function of ice-floe size. . . . . 63

5.14 Ratio R3D/IPA of γλ of the 3D and IPA simulation. . . . . . . . . . . . . . . . 65

5.15 Single logarithmic frequency distributions of γλ from simulated scenarios. . . 68

5.16 Frequency distributions of γλ measurements and simulation. . . . . . . . . . . 69

5.17 Retrieval results of γλ as a function of the distance to the ice edge. . . . . . . 70

5.18 Overestimation of τst and reff as a function of the distance to the ice edge. . . 71

5.19 Cloud optical thickness of Arctic Stratus on 14 May 2012. . . . . . . . . . . . 73

6.1 Spatial auto–correlation function P 2τ (Lxy) of fields of τ . . . . . . . . . . . . . 78

6.2 AisaEAGLE images, corresponding 2D power spectral density E(kx,y), and 1D

power spectral density E(kx,y) along and across prevailing direction of scale

invariant areas for inhomogeneous cloud case without directional structure,

homogeneous cloud case with slight directional structure, and inhomogeneous

cloud case with distinct directional structure. . . . . . . . . . . . . . . . . . . 82

6.3 1D power spectral density E(ky) (gray dots) for each spatial pixel on the swath

axis of the τ field from (a) case C-01 and (b) case V-07. Scale-invariant slopes

β are marked with colored solid lines. The E(krn) derived from the octave

binning are included as black squares. Scale breaks ξτ,L and ξτ,s are indicated

by dashed lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

List of Tables 111

List of Tables

1.1 Category of remote-sensing techniques, instruments, and spatial resolution/-

coverage. The spectral instrumental characteristics are indicated by index B

(bands) and M (multi-spectral). . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.1 Summarized specifications of the imaging spectrometer AisaEAGLE. . . . . . 21

3.2 Emission lines of spectral lamps. . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Detectable scattering angle range from AisaEAGLE measurements of the solar

spectral radiance I↓λ and I↑λ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1 Instrumentation at the BCO during the CARRIBA campaign. . . . . . . . . 34

4.2 Characteristics of the evaluated measurement periods. . . . . . . . . . . . . . 37

4.3 Relative and absolute difference of retrieved τci compared to benchmark case. 44

5.1 Instrumentation of the Polar–5 aircraft during the VERDI campaign. . . . . . 49

5.2 Summarized distances ∆L and ∆LHPT of the presented case studies. . . . . . 62

5.3 Average and standard deviation of the simulated γλ from the four presented

scenarios for the whole surface albedo field (γλ,total), ice covered areas only

(γλ,ice), and water covered areas only (γλ,water). Simulations performed for

clouds with an optical thickness of τst=1 and τst=5. . . . . . . . . . . . . . . 66

5.4 Ratio R3D/IPA of γλ for the total scene area (Rtotal), for the sea-ice covered

area (Rice), and for the dark ocean covered area (Rwater) of all scenarios from

Sects. 5.4.4 and 5.4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.5 Average and standard deviation (τst ± στ ), measurement period, cloud top

altitude, and size of the retrieved fields of τst from VERDI. . . . . . . . . . . 74

5.6 Forward model errors ∆τst (in %) for different error sources. . . . . . . . . . . 74

6.1 Mean and standard deviation (τ ±στ ) and inhomogeneity parameters (ρτ , Sτ ,

χτ ) calculated for retrieved fields of τ from CARRIBA and VERDI. . . . . . 76

6.2 De–correlation length of retrieved fields of τ from CARRIBA and VERDI. . . 80

6.3 Scale breaks calculated for the retrieved fields of τ from CARRIBA and VERDI. 84

Acknowledgements 113

Acknowledgements

This work was performed at the University of Leipzig and was partly funded by the German

Research Foundation (Deutsche Forschungsgemeinschaft, DFG) as part of the CARRIBA

project (WE 1900/18-1 and SI 1534/3-1).

I am grateful to the Max Planck Institute for Meteorology, Hamburg for supporting the

ground-based radiation measurements with the infrastructure of the Barbados Cloud Obser-

vatory at Deebles Point on Barbados.

I am further grateful to the Alfred Wegener Institute Helmholtz Centre for Polar and Marine

Research, Bremerhaven for supporting the VERDI campaign with the aircraft and manpower.

In addition I like to thank Kenn Borek Air Ltd., Calgary, Canada for the great pilots who

made the complicated measurements possible.

I wish to thank the many people who helped with either their expertise or with kind words

and who were indispensable for finishing this thesis. First and foremost I want to thank

my supervisor Manfred Wendisch, who did a great job supporting me during the last years.

Especially in the beginning, my former colleague Eike Bierwirth supported me a lot regarding

the instruments handling and in addition introduced me to the data evaluation programs.

My colleagues Andre Ehrlich, Evi Jakel, and Tim Carlsen provided guidance when ever I got

stuck and in addition often found the right words which in turn helped this thesis to become

better.

I also want to thank my family. Right from the start, they always believed in me and

my plans and helped me to find the right way. My friends, namely Christian, Bene, Sara,

and especially Juliane also deserve credit. Their encouraging words helped a lot to keep on

working and to achieve my personal goals.

Curriculum Vitae 115

Curriculum Vitae

Name Michael Schafer

Date of birth 27 February 1985

Place of birth Schonebeck/ Elbe, Sachsen–Anhalt

Citizenship German

Current address Gorkistr. 120

04347 Leipzig, Germany

Email: micha.meteorologe (at) web.de

Education

1991 – 1995 Basic Primary School, Biere

1995 – 1997 Secondary School, Welsleben

1997 – 2004 Dr.–Tolberg–Grammar School, Schonebeck/ Elbe

Degree: Abitur

10/2005 – 02/2011 Meteorology at the University of Leipzig, Germany

Degree: Diploma

01/2012 – present PhD student at the University of Leipzig, Germany

Employments

09/2003–09/2004 Assistant employee at Erdgas Mittelsachsen GmbH, Schonebeck/ Elbe

10/2004–06/2005 Basic military service

12/2008–03/2011 Student assistant at Leibniz Institute for Tropospheric Research,

Leipzig, Germany

04/2011–12/2011 Research assistant at Leibniz Institute for Tropospheric Research,

Leipzig, Germany

01/2012 – present Scientific employee at University of Leipzig, Germany

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